text:
# GeneralizedExtremeValueDistribution

Generalized extreme value probability distribution object

## Description

A GeneralizedExtremeValueDistribution object consists of parameters, a model description, and sample data for a generalized extreme value probability distribution.

The generalized extreme value distribution is often used to model the smallest or largest value among a large set of independent, identically distributed random values representing measurements or observations. It combines three simpler distributions into a single form, allowing a continuous range of possible shapes that include all three of the simpler distributions.

The three distribution types correspond to the limiting distribution of block maxima from different classes of underlying distributions:

• Type 1 — Distributions whose tails decrease exponentially, such as the normal distribution

• Type 2 — Distributions whose tails decrease as a polynomial, such as Student’s t distribution

• Type 3 — Distributions whose tails are finite, such as the beta distribution

The generalized extreme value distribution uses the following parameters.

ParameterDescriptionSupport
kShape parameter$-\infty \le k\le \infty$
sigmaScale parameter$\sigma \ge 0$
muLocation parameter$-\infty \le \mu \le \infty$

## Creation

There are several ways to create a GeneralizedExtremeValueDistribution probability distribution object.

• Create a distribution with specified parameter values using makedist.

• Fit a distribution to data using fitdist.

• Interactively fit a distribution to data using the Distribution Fitter app.

## Properties

expand all

### Distribution Parameters

Shape parameter of the generalized extreme value distribution, specified as a scalar value.

Data Types: single | double

Scale parameter of the generalized extreme value distribution, specified as a nonnegative scalar value.

Data Types: single | double

Location parameter of the generalized extreme value distribution, specified as a scalar value.

Data Types: single | double

### Distribution Characteristics

This property is read-only.

Logical flag for truncated distribution, specified as a logical value. If IsTruncated equals 0, the distribution is not truncated. If IsTruncated equals 1, the distribution is truncated.

Data Types: logical

This property is read-only.

Number of parameters for the probability distribution, specified as a positive integer value.

Data Types: double

This property is read-only.

Covariance matrix of the parameter estimates, specified as a p-by-p matrix, where p is the number of parameters in the distribution. The (i,j) element is the covariance between the estimates of the ith parameter and the jth parameter. The (i,i) element is the estimated variance of the ith parameter. If parameter i is fixed rather than estimated by fitting the distribution to data, then the (i,i) elements of the covariance matrix are 0.

Data Types: double

This property is read-only.

Logical flag for fixed parameters, specified as an array of logical values. If 0, the corresponding parameter in the ParameterNames array is not fixed. If 1, the corresponding parameter in the ParameterNames array is fixed.

Data Types: logical

This property is read-only.

Distribution parameter values, specified as a vector.

Data Types: single | double

This property is read-only.

Truncation interval for the probability distribution, specified as a vector containing the lower and upper truncation boundaries.

Data Types: single | double

### Other Object Properties

This property is read-only.

Probability distribution name, specified as a character vector.

Data Types: char

This property is read-only.

Data used for distribution fitting, specified as a structure containing the following:

• data: Data vector used for distribution fitting.

• cens: Censoring vector, or empty if none.

• freq: Frequency vector, or empty if none.

Data Types: struct

This property is read-only.

Distribution parameter descriptions, specified as a cell array of character vectors. Each cell contains a short description of one distribution parameter.

Data Types: char

This property is read-only.

Distribution parameter names, specified as a cell array of character vectors.

Data Types: char

## Object Functions

 cdf Cumulative distribution function icdf Inverse cumulative distribution function iqr Interquartile range mean Mean of probability distribution median Median of probability distribution negloglik Negative loglikelihood of probability distribution paramci Confidence intervals for probability distribution parameters pdf Probability density function proflik Profile likelihood function for probability distribution random Random numbers std Standard deviation of probability distribution truncate Truncate probability distribution object var Variance of probability distribution

## Examples

collapse all

Create a generalized extreme value distribution object using the default parameter values.

pd = makedist('GeneralizedExtremeValue')
pd =
GeneralizedExtremeValueDistribution

Generalized Extreme Value distribution
k = 0
sigma = 1
mu = 0

Create a generalized extreme value distribution object by specifying values for the parameters.

pd = makedist('GeneralizedExtremeValue','k',0,'sigma',2,'mu',1)
pd =
GeneralizedExtremeValueDistribution

Generalized Extreme Value distribution
k = 0
sigma = 2
mu = 1

Compute the mean of the distribution.

m = mean(pd)
m = 2.1544

Download ebook


text:
## Buletinul Academiei de Științe a Republicii Moldova. Matematica

 Short Title: Bul. Acad. Științe Repub. Mold., Mat. Parallel Title: Izvestiya Akademii Nauk Respubliki Moldova. Matematika Publisher: Academy of Sciences of Moldova, Institute of Mathematics and Computer Science (IMCS), Chișinău ISSN: 1024-7696; 0236-3089/e Online: http://www.math.md/publications/basm/issues/http://www.mathnet.ru/php/journal.phtml?jrnid=basm&option_lang=eng Predecessor: Izvestiya Akademii Nauk Moldavskoĭ SSR. Seriya Fiziko-Tekhnicheskikh i Matematicheskikh Nauk Comments: Indexed cover-to-cover; Partly continuation from: This journal is available open access.
 Documents Indexed: 979 Publications (since 1990) References Indexed: 132 Publications with 2,450 References.
all top 5

### Latest Issues

 2022, No. 1(98) (2022) 2021, No. 3(97) (2021) 2021, No. 1(95)-2(96) (2021) 2020, No. 3(94) (2020) 2020, No. 2(93) (2020) 2020, No. 1(92) (2020) 2019, No. 3(91) (2019) 2019, No. 2(90) (2019) 2019, No. 1(89) (2019) 2018, No. 3(88) (2018) 2018, No. 2(87) (2018) 2018, No. 1(86) (2018) 2017, No. 3(85) (2017) 2017, No. 2(84) (2017) 2017, No. 1(83) (2017) 2016, No. 3(82) (2016) 2016, No. 2(81) (2016) 2016, No. 1(80) (2016) 2015, No. 3(79) (2015) 2015, No. 2(78) (2015) 2015, No. 1(77) (2015) 2014, No. 3(76) (2014) 2014, No. 2(75) (2014) 2014, No. 1(74) (2014) 2013, No. 2(72)-3(73) (2013) 2013, No. 1(71) (2013) 2012, No. 3(70) (2012) 2012, No. 2(69) (2012) 2012, No. 1(68) (2012) 2011, No. 3(67) (2011) 2011, No. 2(66) (2011) 2011, No. 1(65) (2011) 2010, No. 3(64) (2010) 2010, No. 2(63) (2010) 2010, No. 1(62) (2010) 2009, No. 3(61) (2009) 2009, No. 2(60) (2009) 2009, No. 1(59) (2009) 2008, No. 3(58) (2008) 2008, No. 2(57) (2008) 2008, No. 1(56) (2008) 2007, No. 3(55) (2007) 2007, No. 2(54) (2007) 2007, No. 1(53) (2007) 2006, No. 3(52) (2006) 2006, No. 2(51) (2006) 2006, No. 1(50) (2006) 2005, No. 3(49) (2005) 2005, No. 1(47) (2005) 2004, No. 3(46) (2004) 2004, No. 2(45) (2004) 2004, No. 1(44) (2004) 2003, No. 2(42) (2003) 2003, No. 1(41) (2003) 2002, No. 3(40) (2002) 2002, No. 2(39) (2002) 2002, No. 1(38) (2002) 2001, No. 3(37) (2001) 2001, No. 2(36) (2001) 2001, No. 1(35) (2001) 2000, No. 3(34) (2000) 2000, No. 2(33) (2000) 1999, No. 3(31) (1999) 1999, No. 2(30) (1999) 1999, No. 1(29) (1999) 1998, No. 3(28) (1998) 1998, No. 2(27) (1998) 1997, No. 3(25) (1997) 1996, No. 3(22) (1996) 1996, No. 2(21) (1996) 1996, No. 1(20) (1996) 1995, No. 2-3(18-19) (1995) 1995, No. 1(17) (1995) 1994, No. 3(16) (1994) 1994, No. 2(15) (1994) 1994, No. 1(14) (1994) 1993, No. 3(13) (1993) 1993, No. 2(12) (1993) 1993, No. 1(11) (1993) 1992, No. 4(10) (1992) 1992, No. 3(9) (1992) 1992, No. 2(8) (1992) 1992, No. 1(7) (1992) 1991, No. 2(5) (1991) 1991, No. 1(4) (1991) 1990, No. 3(3) (1990) 1990, No. 2(2) (1990) 1990, No. 1(1) (1990)
all top 5

all top 5

### Fields

 160 Ordinary differential equations (34-XX) 148 Associative rings and algebras (16-XX) 137 Group theory and generalizations (20-XX) 91 General topology (54-XX) 72 Operations research, mathematical programming (90-XX) 47 Topological groups, Lie groups (22-XX) 47 Operator theory (47-XX) 43 Partial differential equations (35-XX) 42 Combinatorics (05-XX) 42 Dynamical systems and ergodic theory (37-XX) 33 Numerical analysis (65-XX) 33 Mechanics of deformable solids (74-XX) 32 Mathematical logic and foundations (03-XX) 32 Probability theory and stochastic processes (60-XX) 31 Differential geometry (53-XX) 30 History and biography (01-XX) 30 Order, lattices, ordered algebraic structures (06-XX) 27 Functions of a complex variable (30-XX) 26 Convex and discrete geometry (52-XX) 26 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 24 General algebraic systems (08-XX) 24 Geometry (51-XX) 23 Functional analysis (46-XX) 21 Integral equations (45-XX) 20 Computer science (68-XX) 20 Fluid mechanics (76-XX) 18 Number theory (11-XX) 17 Commutative algebra (13-XX) 17 Systems theory; control (93-XX) 16 Calculus of variations and optimal control; optimization (49-XX) 15 Information and communication theory, circuits (94-XX) 14 Nonassociative rings and algebras (17-XX) 13 Several complex variables and analytic spaces (32-XX) 13 Statistical mechanics, structure of matter (82-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 11 Manifolds and cell complexes (57-XX) 10 Category theory; homological algebra (18-XX) 10 Difference and functional equations (39-XX) 9 Algebraic geometry (14-XX) 8 Real functions (26-XX) 8 Biology and other natural sciences (92-XX) 7 Approximations and expansions (41-XX) 7 Global analysis, analysis on manifolds (58-XX) 7 Statistics (62-XX) 6 Classical thermodynamics, heat transfer (80-XX) 4 Field theory and polynomials (12-XX) 4 Sequences, series, summability (40-XX) 3 General and overarching topics; collections (00-XX) 3 Abstract harmonic analysis (43-XX) 3 Algebraic topology (55-XX) 3 Mechanics of particles and systems (70-XX) 3 Quantum theory (81-XX) 3 Relativity and gravitational theory (83-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Geophysics (86-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX)

### Citations contained in zbMATH Open

269 Publications have been cited 569 times in 428 Documents Cited by Year
Integrals and phase portraits of planar quadratic differential systems with invariant lines of total multiplicity four. Zbl 1159.34329
Schlomiuk, Dana; Vulpe, Nicolae
2008
Global attractors of infinite-dimensional nonautonomous dynamical systems. I. Zbl 1115.37361
Cheban, D. N.
1997
On rational bases of $$\text{GL} (2,\mathbb{R})$$-comitants of planar polynomial systems of differential equations. Zbl 1050.34049
Calin, Iurie
2003
Chebyshev-Grüss-type inequalities via discrete oscillations. Zbl 1305.26040
Gonska, Heiner; Raşa, Ioan; Rusu, Maria-Daniela
2014
On subsemimodules of semimodules. Zbl 1201.16037
Ebrahimi Atani, Reza; Ebrahimi Atani, Shahabaddin
2010
Algebraic equations with invariant coefficients in qualitative study of the polynomial homogeneous differential systems. Zbl 1051.34022
Baltag, Valeriu
2003
Open problems on the algebraic limit cycles of planar polynomial vector fields. Zbl 1280.34035
Llibre, Jaume
2008
Affine-invariant conditions for determining the number and multiplicity of singular points of quadratic differential systems. Zbl 0842.34028
Baltag, V. A.; Vulpe, N. I.
1993
Free rectangular tribands. Zbl 1352.08004
Zhuchok, Yuliia V.
2015
Central and medial quasigroups of small order. Zbl 1349.20075
Stanovský, David; Vojtěchovský, Petr
2016
The number of comitants that are involved in determining the number of integral lines of a cubic differential system. Zbl 0895.34022
Popa, M. N.
1990
On cyclically-interval edge colorings of trees. Zbl 1252.05066
Kamalian, R. R.
2012
Ideal theory in commutative semirings. Zbl 1159.16034
Ebrahimi Atani, Reza; Ebrahimi Atani, Shahabaddin
2008
A note on the affine subspaces of three-dimensional Lie algebras. Zbl 1291.93095
Biggs, Rory; Remsing, Claudiu C.
2012
The cubic differential system with six real invariant straight lines along three directions. Zbl 1196.34039
Puţuntică, V.; Şubă, A.
2009
One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities. Zbl 1354.34060
Bujac, Cristina
2015
On certain subclasses of analytic functions associated with generalized Struve functions. Zbl 1353.30014
Murugusundaramoorthy, G.; Janani, T.
2015
Six theorems on six-dimensional Hermitian submanifolds of Cayley algebra. Zbl 1031.53087
Banaru, M.
2000
Invariant lines of a general quadratic differential system. Zbl 0915.34025
Popa, M. N.; Sibirskij, K. S.
1991
Quadratic systems with limit cycles of normal size. Zbl 1050.34038
Cherkas, Leonid A.; Artés, Joan C.; Llibre, Jaume
2003
Cubic systems with seven invariant straight lines of configuration $$(3,3,1)$$. Zbl 1275.34048
Şubă, Alexandru; Repeşco, Vadim; Puţuntică, Vitalie
2012
On stability of multicriteria investment Boolean problem with Wald’s efficiency criteria. Zbl 1308.90104
2014
On stability radius of the multicriteria variant of Markowitz’s investment portfolio problem. Zbl 1244.90205
2011
Global attractors of nonautonomous disperse dynamical systems and differential inclusions. Zbl 1001.37012
Cheban, D. N.; Schmalfuss, B.
1999
On quasigroups with Moufang identity. Zbl 1027.20507
Shcherbacov, V.; Izbash, V.
1998
Conditions for the maximal multiplicity of an integral line of a differential system with homogeneities of $$m$$th order. Zbl 0993.34035
Popa, M. N.
1992
Moment analysis of the telegraph random process. Zbl 1272.60064
Kolesnik, Alexander D.
2012
The centre-focus problem for analytical systems of Liénard-form in degenerate case. Zbl 1053.34029
Le Van Linh; Sadovskiĭ, A. P.
2003
Balaba, I. N.
2004
Absolute asymptotic stability of discrete linear inclusions. Zbl 1081.39002
Cheban, D.; Mammana, C.
2005
Selected old open problems in general topology. Zbl 1300.54001
Arhangel’skii, A. V.
2013
Examples of quasitopological groups. Zbl 1305.22001
Arhangel’skii, Alexander V.; Choban, Mitrofan M.
2013
Measure of quasistability of a vector integer linear programming problem with generalized principle of optimality in the Helder metric. Zbl 1214.90087
Emelichev, Vladimir A.; Platonov, Andrey A.
2008
Geometric configurations of singularities for quadratic differential systems with total finite multiplicity lower than 2. Zbl 1331.37026
Artés, J. C.; Llibre, J.; Schlomiuk, D.; Vulpe, N.
2013
One new class of cubic systems with maximum number of invariant lines omitted in the classification of J. Llibre and N. Vulpe. Zbl 1310.34083
Cristina, Bujac
2014
Multiobjective games and determining Pareto-Nash equilibria. Zbl 1105.90071
Lozovanu, D.; Solomon, D.; Zelikovsky, A.
2005
Global attractors of infinite-dimensional dynamical systems. III. Zbl 1115.37362
Cheban, D. N.; Fakikh, D. S.
1995
The modification of Maysel formula in the stationary thermoelasticity. Zbl 1115.74319
Seremet, V. D.
1997
Measure of stability for a finite cooperative game with a generalized concept of equilibrium. Zbl 1157.91308
Emelichev, V. A.; Gurevsky, E. E.; Platonov, A. A.
2006
Minimum cost multicommodity flows in dynamic networks and algorithms for their findings. Zbl 1136.90006
Fonoberova, Maria; Lozovanu, Dmitrii
2007
A lower bound for a quotient of roots of factorials. Zbl 1213.33006
Mortici, Cristinel
2009
Inclusion properties of certain subclass of univalent meromorphic functions defined by a linear operator associated with the $$\lambda$$-generalized Hurwitz-Lerch zeta function. Zbl 1423.11159
Srivastava, H. M.; Ghanim, F.; El-Ashwah, R. M.
2017
Algorithms for determining the transient and differential matrices in finite Markov processes. Zbl 1201.65015
Lazari, Alexandru
2010
On the number of ring topologies on countable rings. Zbl 1352.54024
Arnautov, V. I.; Ermakova, G. N.
2015
On stability of Pareto-optimal solution of portfolio optimization problem with Savage’s minimax risk criteria. Zbl 1242.90105
2010
On 2-primal Ore extensions over Noetherian $$\sigma(*)$$-rings. Zbl 1222.16016
Bhat, Vijay Kumar
2011
Hopf bifurcations analysis of a three-dimensional nonlinear system. Zbl 1176.34046
Craioveanu, Mircea; Tigan, Gheorghe
2008
On some operations in the lattice of submodules determined by preradicals. Zbl 1248.16006
Kashu, A. I.
2011
Some addition theorems for rectifiable spaces. Zbl 1248.54008
Arhangel’skii, Alexander V.; Choban, Mitrofan M.
2011
Solution of the problem of the centre for a cubic differential system with three invariant straight lines two of which are parallel. Zbl 1036.34033
Şubă, A.; Cozma, D.
2001
An example of ring with non-modular lattice of ring topologies. Zbl 1027.16027
Arnautov, V. I.; Topolă, A. Gh.
1998
Six-dimensional Hermitian submanifolds of Cayley algebra and $$u$$-Sasakian hypersurfaces axiom. Zbl 1047.53042
Banaru, Mihail
2002
Dissipative functional-differential equations. Zbl 0978.34068
Cheban, D. N.
1991
A universal Turing machine with $$10$$ states and $$3$$ symbols. Zbl 0900.68210
Rogozhin, Yu. V.
1992
Injective modules with the direct summand intersection property. Zbl 1065.16502
Vălcan, D.
1999
Global attractors of non-autonomous difference equations. Zbl 1187.39004
Cheban, D.; Mammana, C.; Michetti, E.
2009
An investment problem under multicriteriality, uncertainty and risk. Zbl 1371.90085
2016
Some homomorphic properties of multigroups. Zbl 1388.20074
Ejegwa, P. A.; Ibrahim, A. M.
2017
On the number of metrizable group topologies on countable groups. Zbl 1408.22001
2013
On Lagrange algorithm for reduced algebraic irrationalities. Zbl 1354.11050
Dobrovol’skii, N. M.; Balaba, I. N.; Rebrova, I. Yu.; Dobrovol’skii, N. N.
2016
Applications of algebraic methods in solving the center-focus problem. Zbl 1297.34045
Popa, Mihail N.; Pricop, Victor V.
2013
On the number of group topologies on countable groups. Zbl 1309.22001
2014
Irreducible triangulations of the Möbius band. Zbl 1308.05036
Chávez, María-José; Lawrencenko, Serge; Quintero, Antonio; Villar, María-Trinidad
2014
On some quasi-identities in finite quasigroups. Zbl 1107.20058
Belyavskaya, G.; Diordiev, A.
2005
Commutator subgroup of Sylow 2-subgroups of alternating group and the commutator width in the wreath product. Zbl 1475.20033
Skuratovskii, Ruslan V.
2020
General theory of radicals of topological rings. Zbl 1114.16309
Arnautov, V. I.
1996
Independence and quasiregularity in algebras. I. Zbl 1114.16304
Ciocanu, Gh.
1996
Pareto approximation of the tail by local exponential modeling. Zbl 1122.62035
2007
Discontinuous term of the distribution for Markovian random evolution in $$\mathbb{R}^3$$. Zbl 1119.60084
Kolesnik, Alexander D.
2006
Concordant solutions of linear multidimensional differential equations. Zbl 0840.34069
Gerko, A. I.
1994
Quadratic systems with dicritical points. Zbl 0858.34027
Vulpe, N. I.; Lupan, M. N.
1994
Factorizations in the rings of the block matrices. Zbl 1396.15012
Petrychkovych, Vasyl’; Dzhaliuk, Nataliia
2017
A note on 2-hypersurfaces of the nearly Kählerian six-sphere. Zbl 1400.53069
Abu-Saleem, Ahmad; Banaru, Mihail B.; Banaru, Galina A.
2017
Regularized gradient-projection algorithm for solving one-parameter nonexpansive semigroup, constrained convex minimization and generalized equilibrium problems. Zbl 07141475
Okeke, C. C.; Mewomo, O. T.
2018
Integral equations in identification of external force and heat source density dynamics. Zbl 1427.35352
Dreglea, Aliona I.; Sidorov, Nikolay A.
2018
Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base. Zbl 07141485
Moldovyan, N. A.
2019
New inequalities of Hardy-Hilbert type. Zbl 1200.26026
Das, Namita; Sahoo Srinibas
2010
Estimates of stability radius of multicriteria Boolean problem with Hölder metrics in parameter spaces. Zbl 1349.90632
2015
Generating cubic equations as a method for public encryption. Zbl 1349.11149
Moldovyan, N. A.; Moldovyan, A. A.; Shcherbacov, V. A.
2015
Belousov’s theorem and the quantum Yang-Baxter equation. Zbl 1349.20074
Smith, Jonathan D. H.
2016
Algebras with parastrophically uncancellable quasigroup equations. Zbl 1349.20069
Ehsani, Amir; Krapež, Aleksandar; Movsisyan, Yuri
2016
Soltan, Valeriu
2010
On definitions of groupoids closely connected with quasigroups. Zbl 1176.20065
Shcherbacov, V. A.
2007
The transvectants and the integrals for Darboux systems of differential equations. Zbl 1159.34028
Baltag, Valeriu; Calin, Iurie
2008
Exact solutions for a rotational flow of generalized second-grade fluids through a circular cylinder. Zbl 1166.76005
Mahmood, Amir; Saifullah; Rubab, Qammar
2008
Queuing system evolution in phase merging scheme. Zbl 1167.60360
Korolyk, V.; Mishkoy, Gh.; Mamonova, A.; Griza, Iu.
2008
Convex solids with hyperplanar midsurfaces for restricted families of chords. Zbl 1244.52008
Soltan, Valeriu
2011
Beidar, K. I.; Wiegandt, R.
1999
Zero divisors in group-based algebras. Algebras without zero divisors. Zbl 0971.20048
Plotkin, B.
1999
On the classification of tilings on Riemann surfaces of genus two. Zbl 1031.52006
Zamorzaeva, E. A.
2000
The minimum-cost flow problem on dynamic networks and an algorithm for its solving. Zbl 1115.90317
Lozovanu, D.; Stratila, D.
2001
On the compatibility of the tangency relations of sets of some classes. Zbl 1027.54502
1998
Strengthening the topologies of compact rings. Zbl 0896.54022
Tsarelunga, B. I.
1990
Topology of free topological algebras with the Mal’tsev condition and a $$k$$-space. Zbl 0900.16057
Kiriyak, L. L.
1990
The Levinson center of dispersible dissipative dynamical systems. Zbl 0896.54025
Sulaiman, Fakeeh Derar
1990
Concordant solutions of quasilinear multidimensional differential equations. Zbl 0893.34058
Gerko, A. I.
1995
On applications of Riemannian geometry in theory of the second order ordinary differential equations. Zbl 1078.34508
Dryuma, V. S.
1999
Post-optimal analysis of investment problem with Wald’s ordered maximin criteria. Zbl 1401.90125
2012
Gardner, B. J.; Plant, A.
2009
Note on multiple zeta-values. Zbl 1158.11336
2003
Commutator subgroup of Sylow 2-subgroups of alternating group and the commutator width in the wreath product. Zbl 1475.20033
Skuratovskii, Ruslan V.
2020
New form of the hidden logarithm problem and its algebraic support. Zbl 1458.94271
Moldovyan, D. N.
2020
Commutative weakly tripotent group rings. Zbl 1461.16028
Danchev, Peter V.
2020
Laurent-Padé approximation for locating singularities of meromorphic functions with values given on simple closed contours. Zbl 1450.65029
Maria, Capcelea; Titu, Capcelea
2020
Asymmetric separation of convex sets. Zbl 1454.52005
Soltan, Valeriu
2020
On two stability types for a multicriteria integer linear programming problem. Zbl 1457.90093
Emelichev, Vladimir Alekseevich; Bukhtoyarov, Sergei E.
2020
On the number of topologies on countable skew fields. Zbl 1485.22002
Arnautov, Vladimir Ivanovich; Ermakova, G. N.
2020
On solutions of the kinetic McKean system. Zbl 1477.35104
Dukhnovsky, Sergey
2020
Free left $$k$$-nilpotent $$n$$-tuple semigroups. Zbl 1477.20110
Zhuchok, Anatolii V.; Zhuchok, Yuliia V.; Odintsova, Oksana O.
2020
An analogue of Bremermann’s theorem on finding the Bergman kernel for the Cartesian product of the classical domains $$\mathfrak{R}_I$$(m, k) and $$\mathfrak{R}_{II}$$(n). Zbl 1484.32033
Abdullayev, Jonibek Sh.
2020
Finite non-commutative associative algebras for setting the hidden discrete logarithm problem and post-quantum cryptoschemes on its base. Zbl 07141485
Moldovyan, N. A.
2019
A note on existence results for a nonlinear fourth-order integral boundary value problem. Zbl 1458.34047
2019
Statistical $$\Lambda$$-convergence in intuitionistic fuzzy normed spaces. Zbl 1470.40012
Antal, Reena; Chawla, Meenakshi; Kumar, Vijay
2019
Asymptotically almost periodic and asymptotically almost automorphic vector-valued generalized functions. Zbl 1472.46045
Kostić, Marko
2019
Binary linear programming approach to graph convex covering problems. Zbl 1465.05140
2019
Finite 2-groups with a non-Dedekind non-metacyclic norm of abelian non-cyclic subgroups. Zbl 1452.20013
Lyman, Fedir; Lukashova, Tetyana; Drushlyak, Marina
2019
$$n$$-torsion regular rings. Zbl 1428.16012
Danchev, Peter V.
2019
On the number of topologies on countable fields. Zbl 1439.22001
Arnautov, V. I.; Ermakova, G. N.
2019
Isohedral tilings by 14-, 16- and 18-gons for hyperbolic translation group of genus two. Zbl 1431.52029
Zamorzaeva, Elizaveta
2019
Morita contexts and closure operators in modules. Zbl 1428.16005
Kashu, A. I.
2019
Regularized gradient-projection algorithm for solving one-parameter nonexpansive semigroup, constrained convex minimization and generalized equilibrium problems. Zbl 07141475
Okeke, C. C.; Mewomo, O. T.
2018
Integral equations in identification of external force and heat source density dynamics. Zbl 1427.35352
Dreglea, Aliona I.; Sidorov, Nikolay A.
2018
Quotient structure and chain conditions on quasi modules. Zbl 1453.13037
Jana, Sandip; Mazumder, Supriyo
2018
On statistical convergence in generalized lacunary sequence spaces. (On statistical convergence in generalized Lacunary sequence spaces.) Zbl 1434.40007
Raj, K.; Anand, R.
2018
Aspects of stability for multicriteria quadratic problems of Boolean programming. Zbl 1427.90203
Emelichev, Vladimir A.; Nikulin, Yury V.
2018
On the solvability of a class of boundary value problems for systems of the integral equations with power nonlinearity on the whole axis. Zbl 1432.45005
Khachatryan, Kh. A.; Andriyan, S. M.; Sisakyan, A. A.
2018
Isohedral tilings by 8-, 10- and 12-gons for hyperbolic translation group of genus two. Zbl 1431.52028
Zamorzaeva, Elizaveta
2018
Later developments based on some ideas of Andrunachievici: special radicals and the lemma. Zbl 1426.16017
Gardner, B. J.
2018
Shape dimension of maps. Zbl 1397.55008
Gevorgyan, P. S.; Pop, I.
2018
Orthogonality and retract orthogonality of operations. Zbl 1396.20078
Fryz, Iryna
2018
Properties of finite unrefinable chains of ring topologies for nilpotent rings. Zbl 1398.16040
Arnautov, V. I.; Ermakova, G. N.
2018
Inclusion properties of certain subclass of univalent meromorphic functions defined by a linear operator associated with the $$\lambda$$-generalized Hurwitz-Lerch zeta function. Zbl 1423.11159
Srivastava, H. M.; Ghanim, F.; El-Ashwah, R. M.
2017
Some homomorphic properties of multigroups. Zbl 1388.20074
Ejegwa, P. A.; Ibrahim, A. M.
2017
Factorizations in the rings of the block matrices. Zbl 1396.15012
Petrychkovych, Vasyl’; Dzhaliuk, Nataliia
2017
A note on 2-hypersurfaces of the nearly Kählerian six-sphere. Zbl 1400.53069
Abu-Saleem, Ahmad; Banaru, Mihail B.; Banaru, Galina A.
2017
A new characterization of curves in Euclidean 4-space $$\mathbb{E}^{4}$$. Zbl 1392.53007
Öztürk, Günay; Gürpınar, Selin; Arslan, Kadri
2017
Unrefinable chains when taking the infimum in the lattice of ring topologies for a nilpotent ring. Zbl 1394.16052
Arnautov, V. I.; Ermakova, G. N.
2017
Semi-symmetric isotopic closure of some group varieties and the corresponding identities. Zbl 1400.20019
Krainichuk, Halyna; Tarkovska, Olena
2017
Viscous flow through a porous medium filled by liquid with varying viscosity. Zbl 1401.76041
Filippov, Anatoly; Koroleva, Yulia
2017
Invariant conditions of stability of unperturbed motion governed by some differential systems in the plane. Zbl 1400.34092
Neagu, Natalia; Victor, Orlov; Mihail, Popa
2017
Forbidden set of the rational difference equation $$x_{n+1}=x_nx_{n-k}/(ax_{n-k+1}+x_n x_{n-k+1}x_{n-k})$$. Zbl 1390.39019
Rabago, Julius Fergy T.
2017
On the inverse operations in the class of preradicals of a module category. I. Zbl 1390.16005
Jardan, Ion
2017
Central and medial quasigroups of small order. Zbl 1349.20075
Stanovský, David; Vojtěchovský, Petr
2016
An investment problem under multicriteriality, uncertainty and risk. Zbl 1371.90085
2016
On Lagrange algorithm for reduced algebraic irrationalities. Zbl 1354.11050
Dobrovol’skii, N. M.; Balaba, I. N.; Rebrova, I. Yu.; Dobrovol’skii, N. N.
2016
Belousov’s theorem and the quantum Yang-Baxter equation. Zbl 1349.20074
Smith, Jonathan D. H.
2016
Algebras with parastrophically uncancellable quasigroup equations. Zbl 1349.20069
Ehsani, Amir; Krapež, Aleksandar; Movsisyan, Yuri
2016
On invariants and canonical form of matrices of second order with respect to semiscalar equivalence. Zbl 1376.15006
Shavarovskii, B. Z.
2016
Nontrivial convex covers of trees. Zbl 1371.05022
2016
Uniqueness of certain power of a meromorphic function sharing a set with its differential monomial. Zbl 1376.30022
Banerjee, Abhijit; Ahamed, Molla Basir
2016
Operations on level graphs of bipolar fuzzy graphs. Zbl 1355.05205
Dudek, Wieslaw A.; Talebi, Ali A.
2016
On pseudoisomorphy and distributivity of quasigroups. Zbl 1362.20047
Sokhatsky, Fedir M.
2016
On spectrum of medial $$T_{2}$$-quasigroups. Zbl 1362.20046
Scerbacova, A. V.; Shcherbacov, V. A.
2016
The multiplicative Zagreb co-indices on two graph operators. Zbl 1355.05087
Deldar, Mansoureh; Alaeiyan, Mehdi
2016
Lattice of all topologies of countable module over countable rings. Zbl 1355.16043
2016
Free rectangular tribands. Zbl 1352.08004
Zhuchok, Yuliia V.
2015
One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities. Zbl 1354.34060
Bujac, Cristina
2015
On certain subclasses of analytic functions associated with generalized Struve functions. Zbl 1353.30014
Murugusundaramoorthy, G.; Janani, T.
2015
On the number of ring topologies on countable rings. Zbl 1352.54024
Arnautov, V. I.; Ermakova, G. N.
2015
Estimates of stability radius of multicriteria Boolean problem with Hölder metrics in parameter spaces. Zbl 1349.90632
2015
Generating cubic equations as a method for public encryption. Zbl 1349.11149
Moldovyan, N. A.; Moldovyan, A. A.; Shcherbacov, V. A.
2015
Determining the optimal evolution time for Markov processes with final sequence of states. Zbl 1361.65007
Lazari, Alexandru
2015
The Cotton tensor and Chern-Simons invariants in dimension 3: an introduction. Zbl 1355.58008
Moroianu, Sergiu
2015
Relation between Levinson center, chain recurrent set and center of Birkhoff for compact dissipative dynamical systems. Zbl 1376.37038
Cheban, David
2015
On soft trees. Zbl 1349.05332
2015
Rational bases of $$\mathrm{GL}(2,\mathbb{R})$$-comitants and of $$\mathrm{GL}(2,\mathbb{R})$$-invariants for the planar system of differential equations with nonlinearities of the fourth degree. Zbl 1354.34065
Stanislav, Ciubotaru
2015
Third Hankel determinant for the inverse of reciprocal of bounded turning functions. Zbl 1353.30016
Venkateswarlu, B.; Krishna, D. Vamshee; Rani, N.
2015
Determining the distribution of the duration of stationary games for zero-order Markov processes with final sequence of states. Zbl 1349.91032
Lazari, Alexandru
2015
A parametric scheme for online uniform-machine scheduling to minimize the makespan. Zbl 1349.90338
Dolgui, Alexandre; Kotov, Vladimir; Quilliot, Alain
2015
Chebyshev-Grüss-type inequalities via discrete oscillations. Zbl 1305.26040
Gonska, Heiner; Raşa, Ioan; Rusu, Maria-Daniela
2014
On stability of multicriteria investment Boolean problem with Wald’s efficiency criteria. Zbl 1308.90104
2014
One new class of cubic systems with maximum number of invariant lines omitted in the classification of J. Llibre and N. Vulpe. Zbl 1310.34083
Cristina, Bujac
2014
On the number of group topologies on countable groups. Zbl 1309.22001
2014
Irreducible triangulations of the Möbius band. Zbl 1308.05036
Chávez, María-José; Lawrencenko, Serge; Quintero, Antonio; Villar, María-Trinidad
2014
Estimation of the extreme survival probabilities from censored data. Zbl 1308.62189
Grama, Ion; Tricot, Jean-Marie; Petiot, Jean-François
2014
Max-Erlang and min-Erlang power series distributions as two new families of lifetime distribution. Zbl 1308.62026
Leahu, Alexei; Munteanu, Bogdan Gheorghe; Cataranciuc, Sergiu
2014
Bi-deniable public-key encryption protocol which is secure against active coercive adversary. Zbl 1349.11148
Moldovyan, A. A.; Moldovyan, N. A.; Shcherbacov, V. A.
2014
The endomorphism semigroup of a free dimonoid of rank 1. Zbl 1348.08003
Zhuchok, Yurii V.
2014
Equivalence of pairs of matrices with relatively prime determinants over quadratic rings of principal ideals. Zbl 1358.15008
2014
A note on six-dimensional planar Hermitian submanifolds of Cayley algebra. Zbl 1312.53094
Banaru, Mihail B.; Banaru, Galina A.
2014
Interpolating Bézier spline curves with local control. Zbl 1307.65017
Pobegailo, A. P.
2014
Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions. Zbl 1358.47017
Wolf, Elke
2014
On 2-primal Ore extensions over Noetherian weak $$\sigma$$-rigid rings. Zbl 1311.16020
Bhat, Vijay Kumar
2014
Compact global attractors of non-autonomous gradient-like dynamical systems. Zbl 1337.37014
Cheban, David
2014
Selected old open problems in general topology. Zbl 1300.54001
Arhangel’skii, A. V.
2013
Examples of quasitopological groups. Zbl 1305.22001
Arhangel’skii, Alexander V.; Choban, Mitrofan M.
2013
Geometric configurations of singularities for quadratic differential systems with total finite multiplicity lower than 2. Zbl 1331.37026
Artés, J. C.; Llibre, J.; Schlomiuk, D.; Vulpe, N.
2013
On the number of metrizable group topologies on countable groups. Zbl 1408.22001
2013
Applications of algebraic methods in solving the center-focus problem. Zbl 1297.34045
Popa, Mihail N.; Pricop, Victor V.
2013
On free groups in classes of groups with topologies. Zbl 1300.22003
Choban, Mitrofan M.; Chiriac, Liubomir L.
2013
Certain differential superordinations using a multiplier transformation and Ruscheweyh derivative. Zbl 1300.30030
Lupaş, Alina Alb
2013
Semilattice decompositions of trioids. Zbl 1316.08002
Zhuchok, Anatolii V.
2013
On cyclically-interval edge colorings of trees. Zbl 1252.05066
Kamalian, R. R.
2012
A note on the affine subspaces of three-dimensional Lie algebras. Zbl 1291.93095
Biggs, Rory; Remsing, Claudiu C.
2012
Cubic systems with seven invariant straight lines of configuration $$(3,3,1)$$. Zbl 1275.34048
Şubă, Alexandru; Repeşco, Vadim; Puţuntică, Vitalie
2012
Moment analysis of the telegraph random process. Zbl 1272.60064
Kolesnik, Alexander D.
2012
Post-optimal analysis of investment problem with Wald’s ordered maximin criteria. Zbl 1401.90125
2012
Instability of solutions for nonlinear functional differential equations of fifth order with $$n$$-deviating arguments. Zbl 1254.34106
Tunç, Cemil
2012
Conjugate sets of loops and quasigroups: $$DC$$-quasigroups. Zbl 1253.20060
Belyavskaya, Galina B.; Popovich, T. V.
2012
Center problem for cubic systems with a bundle of two invariant straight lines and one invariant conic. Zbl 1259.34020
Cozma, Dumitru
2012
...and 169 more Documents
all top 5

### Cited by 539 Authors

 23 Vulpe, Nicolae I. 18 Emelichev, Vladimir Alekseevich 16 Llibre, Jaume 15 Schlomiuk, Dana I. 9 Artés, Joan Carles 9 Zhuchok, Anatolii V. 8 Arnautov, Vladimir Ivanovich 8 Cheban, David Nikolai 7 Banaru, Mikhail Borisovich 7 Bujac, Cristina 6 Biggs, Rory 6 Choban, Mitrofan Mihailovich 6 Ermakova, G. N. 6 Moldovyan, Nikolaĭ Andreevich 6 Remsing, Claudiu-Cristian 6 Shcherbacov, Victor A. 5 Lin, Shou 5 Mammana, Cristiana 5 Petrosyan, Petros A. 5 Sokhatsky, Fedir M. 4 Cozma, Dumitru 4 Kolesnik, Alexander D. 4 Moldovyan, Aleksandr Andreevich 4 Nikulin, Yury V. 4 Şubă, Alexandru 4 Tang, Zhongbao 3 Banaru, Galina Anatol’evna 3 Bhat, Vijay Kumar 3 Duan, Jinqiao 3 Frasin, Basem Aref 3 Gao, Hongjun 3 Gardner, Barry J. 3 Gasull, Armengol 3 Grama, Ion G. 3 Ilić-Georgijević, Emil 3 Korotkov, V. V. 3 Krainichuk, Halyna V. 3 Lazari, Alexandru 3 Lozovanu, Dmitrii 3 Petrichkovich, Vasil’ Mikhaĭlovich 3 Rasa, Ioan 3 Rass, Stefan 3 Rezende, Alex Carlucci 3 Sadovskiĭ, Anton Pavlovich 3 Şeremet, Victor 3 Soltan, Valeriu 3 Tachim Medjo, Theodore 3 Tan, Yijia 3 Tassaddiq, Asifa 3 Ursul, Mihail I. 3 Valero, José 3 Zamorzaeva, Elizaveta 2 Abel, Ulrich 2 Adams, Ross M. 2 Aldawish, Ibtisam 2 Andreev, Alekseĭ Fedorovich 2 Ashrafi, Ali Reza 2 Balaba, Irina Nikolaevna 2 Belyavskaya, Galina Borisovna 2 Bukhtoyarov, Sergei E. 2 Buzatu, Radu 2 Buzzi, Claudio Aguinaldo 2 Calin, Iurie 2 Caraballo Garrido, Tomás 2 Casselgren, Carl Johan 2 Chen, Chaoping 2 Danchev, Peter Vassilev 2 Detchenya, L. V. 2 Dobrovol’skiĭ, Nikolaĭ Mikhaĭlovich 2 Dobrovol’skiĭ, Nikolai Nikolaevich 2 Dzhalyuk, N. S. 2 Ebrahimpour, Mahdieh 2 Ejegwa, Paul Augustine 2 Fonoberova, Maria A. 2 Fryz, Iryna V. 2 Gavrea, Ioan 2 Gerko, A. I. 2 Hrušák, Michael 2 Ivan, Mircea Dumitru 2 Ivanko, Evgeniĭ Evgen’evich 2 Jaíyéọlá, Tèmítọ́pẹ́ Gbọ́láhàn 2 Jardan, Ion 2 Jolaoso, Lateef Olakunle 2 Karabacak, Fatih 2 Kashu, Alekseĭ Ivanovich 2 Khachatrian, Hrant H. 2 Khachatryan, Khachatur Aghavardovich 2 Kharitonov, M. I. 2 Kloeden, Peter Eris 2 König, Sandra 2 Konik, Tadeusz 2 Kuzmin, Kirill G. 2 Lawrencenko, Serge 2 Michetti, Elisabetta 2 Mikhalëv, Aleksandr Vasil’evich 2 Moldovyan, Dmitriĭ Nikolaevich 2 Mortici, Cristinel 2 Mota, Marcos Coutinho 2 Murugusundaramoorthy, Gangadharan 2 Neagu, Natalia ...and 439 more Authors
all top 5

### Cited in 179 Journals

 56 Buletinul Academiei de Științe a Republicii Moldova. Matematica 18 Journal of Mathematical Sciences (New York) 12 Topology and its Applications 12 Qualitative Theory of Dynamical Systems 9 Journal of Differential Equations 8 Journal of Mathematical Analysis and Applications 8 Differential Equations 7 Discrete Mathematics 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Applied Mathematics and Computation 5 Communications in Algebra 5 Mathematical Notes 5 Journal of Algebra 5 Computer Science Journal of Moldova 5 Algebra and Discrete Mathematics 5 Journal of Algebra and its Applications 5 Chebyshevskiĭ Sbornik 4 Chaos, Solitons and Fractals 4 Commentationes Mathematicae Universitatis Carolinae 4 Nonlinear Analysis. Real World Applications 4 Proyecciones 4 European Journal of Pure and Applied Mathematics 4 Diskretnyĭ Analiz i Issledovanie Operatsiĭ 4 Analysis and Mathematical Physics 4 Palestine Journal of Mathematics 3 Discrete Applied Mathematics 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Linear Algebra and its Applications 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Cybernetics and Systems Analysis 3 Trudy Instituta Matematiki 3 Journal of Applied Mathematics and Computing 3 Hacettepe Journal of Mathematics and Statistics 3 Afrika Matematika 2 Acta Mechanica 2 Bulletin of the Australian Mathematical Society 2 Journal of Statistical Physics 2 Rocky Mountain Journal of Mathematics 2 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 2 Advances in Mathematics 2 Geometriae Dedicata 2 Journal of Geometry 2 Journal of Pure and Applied Algebra 2 Results in Mathematics 2 Semigroup Forum 2 Theoretical Computer Science 2 Annals of Operations Research 2 Discrete Mathematics and Applications 2 Aequationes Mathematicae 2 Expositiones Mathematicae 2 Journal of Dynamics and Differential Equations 2 Topological Methods in Nonlinear Analysis 2 Discrete and Continuous Dynamical Systems 2 Positivity 2 Journal of Inequalities and Applications 2 Matematychni Studiï 2 Communications de la Faculté des Sciences de l’Université d’Ankara. Séries A1. Mathematics and Statistics 2 Discrete and Continuous Dynamical Systems. Series B 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Mediterranean Journal of Mathematics 2 Proceedings of the Steklov Institute of Mathematics 2 Journal of Fixed Point Theory and Applications 2 Symmetry 2 Journal of Mathematics 2 International Journal of Analysis 2 AIMS Mathematics 2 Prikladnaya Diskretnaya Matematika 1 Advances in Applied Probability 1 Computers & Mathematics with Applications 1 Information Processing Letters 1 Journal of Engineering Mathematics 1 Linear and Multilinear Algebra 1 Periodica Mathematica Hungarica 1 Physics Letters. B 1 Ukrainian Mathematical Journal 1 Algebra Universalis 1 The Annals of Statistics 1 Computing 1 Czechoslovak Mathematical Journal 1 Demonstratio Mathematica 1 Information Sciences 1 Journal of Applied Probability 1 Journal of the Mathematical Society of Japan 1 Kyungpook Mathematical Journal 1 Mathematica Slovaca 1 Osaka Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Programming and Computer Software 1 Rendiconti del Seminario Matematico della Università di Padova 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 Statistics & Probability Letters 1 Acta Mathematica Hungarica 1 Applied Numerical Mathematics 1 Statistics 1 Discrete & Computational Geometry 1 Extracta Mathematicae 1 Information and Computation ...and 79 more Journals
all top 5

### Cited in 55 Fields

 84 Ordinary differential equations (34-XX) 62 Associative rings and algebras (16-XX) 55 Group theory and generalizations (20-XX) 33 General topology (54-XX) 31 Combinatorics (05-XX) 31 Dynamical systems and ergodic theory (37-XX) 26 Operations research, mathematical programming (90-XX) 24 Topological groups, Lie groups (22-XX) 18 General algebraic systems (08-XX) 18 Partial differential equations (35-XX) 18 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 16 Probability theory and stochastic processes (60-XX) 16 Computer science (68-XX) 15 Differential geometry (53-XX) 13 Number theory (11-XX) 13 Nonassociative rings and algebras (17-XX) 12 Commutative algebra (13-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 12 Approximations and expansions (41-XX) 12 Operator theory (47-XX) 12 Information and communication theory, circuits (94-XX) 11 Order, lattices, ordered algebraic structures (06-XX) 11 Global analysis, analysis on manifolds (58-XX) 10 Fluid mechanics (76-XX) 9 Real functions (26-XX) 9 Functions of a complex variable (30-XX) 9 Convex and discrete geometry (52-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 7 Algebraic geometry (14-XX) 7 Functional analysis (46-XX) 7 Systems theory; control (93-XX) 6 Mathematical logic and foundations (03-XX) 6 Special functions (33-XX) 6 Difference and functional equations (39-XX) 6 Numerical analysis (65-XX) 6 Biology and other natural sciences (92-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Manifolds and cell complexes (57-XX) 5 Statistics (62-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 4 Category theory; homological algebra (18-XX) 4 Mechanics of deformable solids (74-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Geophysics (86-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 3 Geometry (51-XX) 3 Algebraic topology (55-XX) 3 Mechanics of particles and systems (70-XX) 3 Statistical mechanics, structure of matter (82-XX) 2 Sequences, series, summability (40-XX) 2 Quantum theory (81-XX) 1 Field theory and polynomials (12-XX) 1 Measure and integration (28-XX)

format: plain


text:
# Definitions

##### King's shortest paths criterion

The first way to define a ring has been given by Shirley V. King [1] (and later by Franzblau [2]). In order to study the connectivity of glassy SiO$$_2$$ she defines a ring as the shortest path between two of the nearest neighbors of a given node [Fig. 5.13].

In the case of the King's criterion one can calculate the maximum number of different ring sizes, $$NS_{max}(KSP)$$, which can be found using the atom At to initiate the search: $\label{lmaxsp} NS_{max}(KSP)\ =\ \frac{Nc({\textbf{At}}) \times (Nc({\textbf{At}})-1)}{2}$ where $$N_c({\textbf{At}})$$ is the number of neighbors of atom At. $$NS_{max}(KSP)$$ represents the number of ring sizes found if all couples of neighbors of atom At are connected together with paths of different sizes.
It is also possible to calculate the theoretical maximum size, $$TMS(KSP)$$, of a King's shortest path ring in the network using: $\label{tmsking} TMS(KSP)\ = 2\ \times\ (D_{max}\ -\ 2)\ \times (Nc_{max}\ -\ 2)\ +\ 2\ \times\ D_{max}$ where $$D_{max}$$ is the longest distance, in number of chemical bonds, separating two atoms in the network, and $$Nc_{max}$$ represents the average number of neighbors of the chemical species of higher coordination. If used when looking for rings, periodic boundary conditions have to be taken into account to calculate $$D_{max}$$. The relation [Eq. [tmsking]] is illustrated in figure 5.16-2).

##### Guttman's shortest paths criterion

A later definition of ring was proposed by Guttman [3], who defines a ring as the shortest path which comes back to a given node (or atom) from one of its nearest neighbors [Fig. 5.14].

Differences between the King and the Guttman's shortest paths criteria are illustrated in figure 5.15.

Like for the King's criterion, with the Guttman's criterion one can calculate the maximum number of different ring sizes, $$NS_{max}(GSP)$$, which can be found using the atom At to initiate the search: $NS_{max}(GSP) = N_c({\textbf{At}}) - 1$ where $$N_c({\textbf{At}})$$ is the number of neighbors of atom At. $$NS_{max}(GSP)$$ represents the number of ring sizes found if the neighbors of atom At are connected together with paths of different sizes.
It is also possible to calculate the Theoretical Maximum Size, $$TMS(GSP)$$, of a Guttman's ring in the network using: $\label{tmsg} TMS(GSP)\ = 2\ \times\ D_{max}$ where $$D_{max}$$ represents the longest distance, in number of chemical bonds, separating two atoms in the network. If used when looking for rings, periodic boundary conditions have to be taken into account to calculate $$D_{max}$$. The relation [Eq. [tmsg]] is illustrated in figure 5.16-1.

Since the introduction of the King's and the Guttman's criteria other definitions of rings have been proposed. These definitions are based on the properties of the rings to be decomposed into the sum of smaller rings.

##### The primitive rings criterion

A ring is primitive [4], [5] (or Irreducible [6]) if it can not be decomposed into two smaller rings [Fig. 5.17].

The primitive rings analysis between the paths in figure 5.17 may lead to 3 results depending on the relations between the paths A, B, and C:

• If paths A, B, and C have the same length: A = B = C then the rings 'AB', 'AC' and 'BC' are primitives.

• If the relation between the paths is like $$?=?<?$$ (ex: A = B < C) then 1 smaller ring ('AB') and 2 bigger rings ('AC' and 'BC') exist. None of these rings can be decomposed into the sum of two smaller rings therefore the 3 rings are again primitives.

• If the relation between the path is like $$?<?=?$$ (ex: A < B = C) or $$?<?<?$$ (ex: A < B < C) then a shortest path exists (A). It will be possible to decompose the ring ('BC') built without this shortest path into the sum of 2 smaller rings ('AB' and 'AC'), therefore this ring will not be primitive.

##### The strong rings criterion

The strong rings [4], [5] are defined by extending the definition of primitive rings. A ring is strong if it can not be decomposed into a sum of smaller rings whatever this sum is, ie. whatever the number of paths in the decomposition is.

By definition the strong rings are also primitives, therefore to search for strong rings can be summed as to find the strong rings among the primitive rings. This technique is limited to relatively simple cases, like crystals or structures such as the one illustrated in figure 5.18. On the one hand the CPU time needed to complete such an analysis for amorphous systems is very important. On the other hand it is not possible to search for strong rings using the same search depth than for other types of rings. The strong ring analysis is indeed diverging which makes it very complex to implement for amorphous materials.
In the case of primitive rings like in the case of strong rings, there is no theoretical maximum size of rings in the network.

1. S. V. King, Nat., vol. 213, p. 1112, 1967.
2. D. S. Franzblau, Phys. Rev. B., vol. 44, no. 10, pp. 4925–4930, 1991.
3. L. Guttman, J. Non-Cryst. Solids, vol. 116, pp. 145–147, 1990.
4. K. Goetzke and H. J. Klein, J. Non-Cryst. Solids, vol. 127, pp. 215–220, 1991.
5. X. Yuan and A. N. Cormack, Comp. Mat. Sci., vol. 24, pp. 343–360, 2002.
6. F. Wooten, Act. Cryst. A, vol. 58, no. 4, pp. 346–351, 2002.


text:
# O'Neil's problem 2.10 on Tensor Derivations. Literature on the subject.

I am having real trouble trying to understand a problem in O'Neil's "Semi-Riemannian Geometry" and I can't find much literature on the subject. I will expose the problem and I will be grateful to accept hints, solutions and bibliographic sources on tensor derivations.

Problem 2.10 (p.53) Prove that a tensor derivation $\mathfrak{D}$ has $\mathfrak{D}_0 ^0 = 0$ if and only if $\mathfrak{D}_0^1$ is $\mathfrak{F}(M)$- linear (here, $\mathfrak{F}(M)$ stands for all smooth real-valued functions on $M$). Then by interpretation, $\mathfrak{D}_0 ^1 = B \in \mathfrak{T}_1^1(M)$ (where $\mathfrak{T}_s^r(M)$ stands for all (r,s)-tensors on $M$), and we write $\mathfrak{D} = \mathfrak{D}_B$.

Here is the definition of a tensor derivation according to the book:

Definition (Tensor derivation). A tensor derivation $\mathfrak{D}$ is a set of $\mathbb{R}$-linear functions on a smooth manifold $M$ $$\mathfrak{D} = \mathfrak{D}^r_s:\mathfrak{T}_s^r \to \mathfrak{T}_s^r \quad\quad (r\geq 0, s\geq 0)$$ such that for any tensors $A$ and $B$:

(1) $\quad \mathfrak{D}(A \otimes B)= \mathfrak{D}A \otimes B+ A \otimes \mathfrak{D}B$

(2) $\quad \mathfrak{D}(\mathbf{C} A) = \mathbf{C}(\mathfrak{D} A )$ for any contraction $\mathbf{C}$.

My first problem is that I cannot see the intuition behind the definition whose notation is already cumbersome and I cannot find additional literature on the subject. Anyway, I believe a solution to the problem is given by the identity (1), for if $\theta$ is a $(1,0)$-tensor and $f$ a smooth real-valued function then $\mathfrak{D}(f)=\mathfrak{D}_0^0(f)=0$ by hypothesis and (1) becomes (hope this makes some sense): $$\mathfrak{D}(f \theta) = \mathfrak{D}(f) \otimes \theta + f \mathfrak{D}(\theta) = f \mathfrak{D}(\theta)$$ which I hope is enough to prove the necessity and sufficiency of $\mathfrak{F}(M)$-linearity.

Yet I cannot derive how it can be interpreted that $\mathfrak{D}_0^1$ is a (1,1)-tensor! Can anyone explain it? Does someone know a more comprehensive and introductory reference?.

Your argument to show that $D^1_0$ is $\mathcal F(M)$-linear if and only if $D_0^0=0$ using the product rule is completely correct. Now consider the properties of $D^1_0$ in this case: it is an $\mathcal F(M)$-linear bundle map $TM \to TM$, and thus $$B : (X,\omega) \mapsto \omega(D^1_0 X)$$ is an $\mathcal F(M)$-linear map $TM \otimes TM^* \to \mathcal F(M)$; i.e. a $(1,1)$-tensor. (Depending on your definition of $(1,1)$ tensor this may require the additional step of showing that $\mathcal F(M)$-linear maps on tensor products of the tangent bundle correspond to smooth tensor fields; but I assume you're aware of this correspondence.)


text:
# Adding and Subtracting Mixed Numbers

Lesson

Fractions pop up in so many different places everyday. We use fractions when dealing with decimals, percentages, rates, ratios, lengths, distances and so on. When figuring out anything from how much change we get at the shop to cutting a cake to simply measuring things, fractions play an important part in our understanding of how many parts anything can be divided into.

## Proper fractions

### Outcomes

#### NA4-2

Understand addition and subtraction of fractions, decimals, and integers


text:
## Calculus: Early Transcendentals (2nd Edition)

The slope of the secant line: m$=2$ represents the average velocity of the object over the time interval $[0,0.5]$.
Graph s(t) by building a table of function values. Plot the points and draw a smooth curve through them. See image. The slope of the secant line: m= $\displaystyle \frac{s(0.5)-s(0)}{0.5-0}= \displaystyle \frac{1}{0.5}=2$. This represents the average velocity of the object over the time interval $[0,0.5]$.


text:
# What is the slope of the line between  (-3,7)  and  (18,-5) ?

Mar 23, 2016

The slope is $m = - \frac{12}{21}$

#### Explanation:

The formula for the slope of a line based upon two coordinate points is

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the coordinate points $\left(- 3 , 7\right) \mathmr{and} \left(18 , - 5\right)$
${x}_{1} = - 3$
${x}_{2} = 18$
${y}_{1} = 7$
${y}_{2} = - 5$

$m = \frac{- 5 - 7}{18 - \left(- 3\right)}$

$m = - \frac{12}{21}$

The slope is $m = - \frac{12}{21}$


text:
## Explain the use of Past Perfect in the non-underlined part

##### This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 218
Joined: 11 Dec 2013
Thanked: 3 times
Followed by:4 members

### Explain the use of Past Perfect in the non-underlined part

by [email protected] » Wed May 07, 2014 5:27 am

Legendary Member
Posts: 774
Joined: 23 Jan 2012
Thanked: 46 times
Followed by:14 members
by aditya8062 » Wed May 07, 2014 6:12 am
Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil, their descendents, popular known as killer bees had migrated as far north as Southern Texas.

A. Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil,

B. In less than 35 years since releasing African honeybees outside Sao Paulo, Brazil,

C. In less than the 35 years since African honeybees had been released outside Sao Paulo, Brazil,

D. It took less than 35 years from the release of African honeybees outside Sao Paulo, Brazil, when

E. It took less than 35 years after the time that African honeybees were released outside Sao Paulo, Brazil, and then
Last edited by aditya8062 on Wed May 07, 2014 10:47 am, edited 1 time in total.

GMAT Instructor
Posts: 15527
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1896 members
GMAT Score:790
by GMATGuruNY » Wed May 07, 2014 9:40 am
Less than 35 years after the release of African honeybees outside Sao Paulo, their descendants had migrated.

TIMELINE:
----release of the honeybees----migration of their descendants----a moment less than 35 years after the release----exactly 35 years after the release----

The migration was completed BEFORE the moment in red.
Thus, at that moment -- less than 35 years after the release of African honeybees outside Sao Paulo -- their descendants HAD MIGRATED.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

Master | Next Rank: 500 Posts
Posts: 218
Joined: 11 Dec 2013
Thanked: 3 times
Followed by:4 members
by [email protected] » Wed May 07, 2014 8:52 pm
Hey Guru,
Why is option D wrong?

Regards,
Mukherjee

GMAT Instructor
Posts: 15527
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1896 members
GMAT Score:790
by GMATGuruNY » Thu May 08, 2014 3:21 am
Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil, their descendants, popularly known as killer bees, had migrated as far north as southern Texas.

(A) Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil,
(B) In less than 35 years since releasing African honeybees outside Sao Paulo, Brazil,
(C) In less than the 35 years since African honeybees had been released outside Sao Paulo, Brazil,
(D) It took less than 35 years from the release of African honeybees outside Sao Paulo, Brazil, when
(E) It took less than the 35 years after the time that African honeybees were released outside Sao Paulo, Brazil, and then
B: Since RELEASING African honeybees outside Sao Paulo, THEIR DESCENDANTS...
The implication here is that THEIR DESCENDANTS were responsible for RELEASING African honeybees outside Sao Paolo.
Not the intended meaning.
Eliminate B.

C: 35 years since African honeybees HAD BEEN RELEASED
If the release of the bees took place on January 1, 1900, then on January 1, 1950, the bees already HAD BEEN RELEASED.
Thus, 35 years since African Honeybees HAD BEEN RELEASED could imply January 1, 1950 + 35 years = January 1, 1985.
Not the intended timeline.
The intended meaning is that the the migration took place LESS THAN 35 YEARS after the release -- sometime BEFORE January 1, 1935.
Eliminate C.

D and E: It took less than 35 years.
Here, it lacks a clear referent.
Eliminate D and E.

In D and E, it seems to be serving as an EXPLETIVE.
An expletive is a placeholder pronoun whose purpose is to DELAY THE SUBJECT.
On the GMAT, the delayed subject typically will be an infinitive phrase or a that-clause.

IT is easy TO LIKE MARY.
Here, it is standing in for to like Mary.
Conveyed meaning:
TO LIKE MARY is easy.

IT was not until last year THAT JOHN BEGAN STUDYING.
Here, it is standing in for that John began studying.
Conveyed meaning:
THAT JOHN BEGAN STUDYING was not until last year.

In D and E, the referent for it is unclear.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 944
Joined: 30 May 2012
Thanked: 8 times
Followed by:5 members
by [email protected] » Sun Jun 21, 2015 1:52 am
GMATGuruNY wrote:
Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil, their descendants, popularly known as killer bees, had migrated as far north as southern Texas.

(A) Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil,
(B) In less than 35 years since releasing African honeybees outside Sao Paulo, Brazil,
(C) In less than the 35 years since African honeybees had been released outside Sao Paulo, Brazil,
(D) It took less than 35 years from the release of African honeybees outside Sao Paulo, Brazil, when
(E) It took less than the 35 years after the time that African honeybees were released outside Sao Paulo, Brazil, and then
B: Since RELEASING African honeybees outside Sao Paulo, THEIR DESCENDANTS...
The implication here is that THEIR DESCENDANTS were responsible for RELEASING African honeybees outside Sao Paolo.
Not the intended meaning.
Eliminate B.

Also, isn't the the construction Since RELEASING African honeybees AWKWARD ? I think, SINCE can't be followed ONLY by VERB-ing or GERUND.

GMAT Instructor
Posts: 15527
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1896 members
GMAT Score:790
by GMATGuruNY » Sun Jun 21, 2015 2:11 am
[email protected] wrote:
B: Since RELEASING African honeybees outside Sao Paulo, THEIR DESCENDANTS...
The implication here is that THEIR DESCENDANTS were responsible for RELEASING African honeybees outside Sao Paolo.
Not the intended meaning.
Eliminate B.

Generally, the agent of an introductory VERBing modifier must be the SUBJECT of the following clause.

SC73 in the OG for Verbal:
After SUFFERING $2 billion in losses and 25,000 layoffs, THE NATION'S SEMICONDUCTOR INDUSTRY appears to have made a long-awaited recovery. Here, the agent of suffering (an introductory VERBing modifier) is the nation's semiconductor industry (the subject of the following clause). Conveyed meaning: THE NATION'S SEMICONDUCTOR INDUSTRY was SUFFERING$2 billion in losses.

B: Since RELEASING African honeybees outside Sao Paulo, THEIR DESCENDANTS...
Here, the agent of releasing (an introductory VERBing modifier) seems to be their descendants (the subject of the following clause).
Conveyed meaning:
THEIR DESCENDANTS were RELEASING African honeybees.
This meaning is nonsensical.
Also, isn't the the construction Since RELEASING African honeybees AWKWARD ? I think, SINCE can't be followed ONLY by VERB-ing or GERUND.
This reasoning is valid: since + VERBing is not a viable construction on the GMAT.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 944
Joined: 30 May 2012
Thanked: 8 times
Followed by:5 members
by [email protected] » Sun Jun 21, 2015 2:12 am
GMATGuruNY wrote:
Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil, their descendants, popularly known as killer bees, had migrated as far north as southern Texas.

(A) Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil,
(B) In less than 35 years since releasing African honeybees outside Sao Paulo, Brazil,
(C) In less than the 35 years since African honeybees had been released outside Sao Paulo, Brazil,
(D) It took less than 35 years from the release of African honeybees outside Sao Paulo, Brazil, when
(E) It took less than the 35 years after the time that African honeybees were released outside Sao Paulo, Brazil, and then
C: 35 years since African honeybees HAD BEEN RELEASED
If the release of the bees took place on January 1, 1900, then on January 1, 1950, the bees already HAD BEEN RELEASED.
Thus, 35 years since African Honeybees HAD BEEN RELEASED could imply January 1, 1950 + 35 years = January 1, 1985.

Not the intended timeline.
The intended meaning is that the the migration took place LESS THAN 35 YEARS after the release -- sometime BEFORE January 1, 1935.
Eliminate C.
In the above quote, couldn't understand ONLY the RED part - the LOGIC behind the CALCULATIONS. Please help!

Also, in C, I think two PAST PERFECT don't make sense in this particular context. Right ?

As for the OA: Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil - it's a NOUN + Noun Modifier construction modifying the following clause,I guess. And the big NOUN Phrase is in RED while the Noun Modifier (here, a prepositional phrase) is in GREEN. Right ?

GMAT Instructor
Posts: 15527
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1896 members
GMAT Score:790
by GMATGuruNY » Sun Jun 21, 2015 2:31 am
[email protected] wrote:
GMATGuruNY wrote: C: 35 years since African honeybees HAD BEEN RELEASED
If the release of the bees took place on January 1, 1900, then on January 1, 1950, the bees already HAD BEEN RELEASED.
Thus, 35 years since African Honeybees HAD BEEN RELEASED could imply January 1, 1950 + 35 years = January 1, 1985.

Not the intended timeline.
The intended meaning is that the the migration took place LESS THAN 35 YEARS after the release -- sometime BEFORE January 1, 1935.
Eliminate C.
In the above quote, couldn't understand ONLY the RED part - the LOGIC behind the CALCULATIONS. Please help!
Do not worry about understanding the calculations.
The reason for your confusion is that the construction in C -- since + SUBJECT + PAST PERFECT -- does not convey a logical meaning.
Keep it simple:
On the GMAT, since + SUBJECT + PAST PERFECT is not a valid construction.
Also, in C, I think two PAST PERFECT don't make sense in this particular context. Right ?
Correct.
As for the OA: Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil - it's a NOUN + Noun Modifier construction modifying the following clause,I guess. And the big NOUN Phrase is in RED while the Noun Modifier (here, a prepositional phrase) is in GREEN. Right ?

Less than 35 years after the release, their descendants had migrated.
Here, the modifier in red is an ADVERB serving to modify the VERB in the following clause (had migrated).
LESS THEN 35 YEARS AFTER THE RELEASE.
The implication is that at some moment less than 35 years after the release, the migration had already been completed.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 944
Joined: 30 May 2012
Thanked: 8 times
Followed by:5 members
by [email protected] » Mon Jun 22, 2015 7:20 am
GMATGuruNY wrote: Keep it simple:
On the GMAT, since + SUBJECT + PAST PERFECT is not a valid construction.
This is PERFECT.Thanks GMATGuruNY!
On the GMAT, SINCE is used with PRESENT PERFECT MOSTLY. Right ?

But apart from this particular use, what are the OTHER VALID usages of SINCE on GMAT - could you please shed some light on this aspect ?
GMATGuruNY wrote: Less than 35 years after the release, their descendants had migrated.
Here, the modifier in red is an ADVERB serving to modify the VERB in the following clause (had migrated).
LESS THAN 35 YEARS AFTER THE RELEASE.
The implication is that at some moment less than 35 years after the release, the migration had already been completed.
Thanks for clarifying. But won't the SC be better if it were -- [IN] Less than 35 years after the release, their descendants had migrated.

Isn't the preposition IN MISSING here ?

Legendary Member
Posts: 944
Joined: 30 May 2012
Thanked: 8 times
Followed by:5 members
by [email protected] » Sat Jun 27, 2015 12:56 pm
@ GMATGuruNY - any thoughts on the above concerns ?

Looking forward to hear from you. Much thanks in advance!

Legendary Member
Posts: 944
Joined: 30 May 2012
Thanked: 8 times
Followed by:5 members
by [email protected] » Wed Jul 08, 2015 2:25 am
[email protected] wrote:
GMATGuruNY wrote: Keep it simple:
On the GMAT, since + SUBJECT + PAST PERFECT is not a valid construction.
This is PERFECT.Thanks GMATGuruNY!
On the GMAT, SINCE is used with PRESENT PERFECT MOSTLY. Right ?

But apart from this particular use, what are the OTHER VALID usages of SINCE on GMAT - could you please shed some light on this aspect ?
GMATGuruNY wrote: Less than 35 years after the release, their descendants had migrated.
Here, the modifier in red is an ADVERB serving to modify the VERB in the following clause (had migrated).
LESS THAN 35 YEARS AFTER THE RELEASE.
The implication is that at some moment less than 35 years after the release, the migration had already been completed.
Thanks for clarifying. But won't the SC be better if it were -- [IN] Less than 35 years after the release, their descendants had migrated.

Isn't the preposition IN MISSING here ?

Hi GMATGuruNY - any feedback on my above questions Sir ?

GMAT Instructor
Posts: 15527
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1896 members
GMAT Score:790
by GMATGuruNY » Wed Jul 08, 2015 3:59 am
[email protected] wrote:
GMATGuruNY wrote: Keep it simple:
On the GMAT, since + SUBJECT + PAST PERFECT is not a valid construction.
This is PERFECT.Thanks GMATGuruNY!
On the GMAT, SINCE is used with PRESENT PERFECT MOSTLY. Right ?

But apart from this particular use, what are the OTHER VALID usages of SINCE on GMAT - could you please shed some light on this aspect ?
GMATGuruNY wrote: Less than 35 years after the release, their descendants had migrated.
Here, the modifier in red is an ADVERB serving to modify the VERB in the following clause (had migrated).
LESS THAN 35 YEARS AFTER THE RELEASE.
The implication is that at some moment less than 35 years after the release, the migration had already been completed.
Thanks for clarifying. But won't the SC be better if it were -- [IN] Less than 35 years after the release, their descendants had migrated.

Isn't the preposition IN MISSING here ?

IN less than 35 years = HOW MUCH TIME was required for the migration to be completed.
Conveyed meaning:
It took less than 35 years for the migration to be completed.
Less than 35 years after the release = WHEN the migration had been completed.
Conveyed meaning:
At a past moment less than 35 years after the release, the migration had already been completed.
The OA intends to convey the latter meaning.
Mitch Hunt
Private Tutor for the GMAT and GRE
[email protected]

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
Student Review #1
Student Review #2
Student Review #3

Legendary Member
Posts: 944
Joined: 30 May 2012
Thanked: 8 times
Followed by:5 members
by [email protected] » Wed Jul 08, 2015 5:51 am
[email protected] wrote:
GMATGuruNY wrote: Keep it simple:
On the GMAT, since + SUBJECT + PAST PERFECT is not a valid construction.
This is PERFECT.Thanks GMATGuruNY!
On the GMAT, SINCE is used with PRESENT PERFECT MOSTLY. Right ?

But apart from this particular use, what are the OTHER VALID usages of SINCE on GMAT - could you please shed some light on this aspect ?
@ GMATGuruNY - can you please shed some light on the above ?

Legendary Member
Posts: 2666
Joined: 14 Jan 2015
Location: Boston, MA
Thanked: 1153 times
Followed by:127 members
GMAT Score:770
by [email protected] » Wed Jul 08, 2015 7:13 am
But apart from this particular use, what are the OTHER VALID usages of SINCE on GMAT - could you please shed some light on this aspect ?
Are you asking for sample OA's that include 'since?' Or are you asking if 'since' could be used in a fundamentally different way than the above example?
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save \$100 off any live Veritas Prep GMAT Course


text:
http://iet.metastore.ingenta.com
1887

## MIMO transmission

• Author(s):
• DOI:

$16.00 (plus tax if applicable) ##### Buy Knowledge Pack 10 chapters for$120.00
(plus taxes if applicable)

IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.

Recommend Title Publication to library

You must fill out fields marked with: *

Librarian details
Name:*
Email:*
Name:*
Email:*
Department:*
Why are you recommending this title?
Select reason:

Introduction to Digital Wireless Communications — Recommend this title to your library

## Thank you

In this chapter, we study the fundamental principles of MIMO transmission and illustrate its performance advantages. We first introduce the flat fading MIMO channel model. Then, we present several MIMO transmission strategies exploring the diversity benefit inherent to MIMO channel. After that, we investigate the capacity potential of MIMO channel and study MIMO transmission strategies extracting the spatial multiplexing gains. The chapter is concluded with a characterization of the diversity-multiplexing trade-off.

Chapter Contents:

• 10.1 MIMO channel model
• 10.2 Diversity over MIMO channels
• 10.2.1 Channel knowledge available at transmitter
• 10.2.2 Channel knowledge unavailable at transmitter
• 10.3 Multiplexing over MIMO channels
• 10.3.1 Parallel decomposition
• 10.3.2 Spatial multiplexing
• 10.3.2.1 Uncoded transmission
• 10.3.2.2 Coded transmission
• Problems
• Bibliography

Inspec keywords:

Preview this chapter:

MIMO transmission, Page 1 of 2

| /docserver/preview/fulltext/books/te/pbte072e/PBTE072E_ch10-1.gif /docserver/preview/fulltext/books/te/pbte072e/PBTE072E_ch10-2.gif

### Related content

content/books/10.1049/pbte072e_ch10
pub_keyword,iet_inspecKeyword,pub_concept
6
6
This is a required field


text:
+0

# help number theory

0
145
2

When the positive integer x is divided by each of 4, 5, 6, and 7, it has a remainder of 3. What is the sum of the three smallest possible values of x?

Jul 9, 2021

#1
0

The sum of the three smallest possible values of x is 858.

Jul 9, 2021
#2
+26226
+2

When the positive integer x is divided by each of 4, 5, 6, and 7,

it has a remainder of 3.
What is the sum of the three smallest possible values of x?

$$\begin{array}{|rcll|} \hline x&\equiv& 3 \pmod{4} \\ x&\equiv& 3 \pmod{5} \\ x&\equiv& 3 \pmod{6} \\ x&\equiv& 3 \pmod{7} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline \text{sum} &=& \Big( 3+0\times \text{lcm}(4,~5,~6,~7) \Big) \\ && +\Big( 3+1\times \text{lcm}(4,~5,~6,~7) \Big) \\ && +\Big( 3+2\times \text{lcm}(4,~5,~6,~7) \Big) \\\\ \text{sum} &=& 3 + ( 3+420 )+( 3+2\times420 ) \\\\ \text{sum} &=& 3 + 423+843 \\ \text{sum} &=& 1269 \\ \hline \end{array}$$

Jul 10, 2021
edited by heureka  Jul 10, 2021


text:
# Body Mass Index

BMI or Body Mass Index is a gross estimate for the amount of fat in your body. It is a number calculated from a person’s weight and height and applies to both men and women between ages of 18 to 65. BMI provides a reliable indicator of body fatness for most people and is used to screen for weight categories that may lead to health problems.

To calculate your BMI, your doctor needs to know your height in metres and weight in Kilograms.
If you would like to have a go at doing it yourself, here’s how:

$mathrm{BMI} = frac{mbox{mass} mbox{(kg)}}{left( mbox{height}(mathrm{m})right)^2}$

1. Multiply your height in metres by your height in metres. For example 1.5 by 1.5 metres gives you 2.25.
2. Then divide your weight in kg by this figure.

So, if you weigh 50 kg, your BMI will be 50 divided by 2.25 = 22.22.
You can also calculate your BMI using our BMI calculator.
Here’s how to classify your BMI:

BMI less than 18.5 – underweight
BMI 18.5 to 22.9 – normal
BMI equal to or more than 23 – overweight
BMI equal to or more than 25 – obese

Calculate your BMI here, the fun way.


text:
Home > Standard Error > Standand Error

# Standand Error

## Contents

You're just very unlikely to be far away if you took 100 trials as opposed to taking five. Relative standard error See also: Relative standard deviation The relative standard error of a sample mean is the standard error divided by the mean and expressed as a percentage. So let's say you were to take samples of n is equal to 10. And then when n is equal to 25, we got the standard error of the mean being equal to 1.87.

Well, Sal, you just gave a formula. We're not going to-- maybe I can't hope to get the exact number rounded or whatever. Here, we're going to do a 25 at a time and then average them. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a non-profit organization. why not try these out

## Standard Error Formula

Let's see if it conforms to our formulas. And then you now also understand how to get to the standard error of the mean.Sampling distribution of the sample mean 2Sampling distribution example problemUp NextSampling distribution example problem Algebra Applied Now, this is going to be a true distribution. The standard deviation of the age was 3.56 years.

And this time, let's say that n is equal to 20. And n equals 10, it's not going to be a perfect normal distribution, but it's going to be close. Published on 2 Dec 2012Paul Andersen shows you how to calculate the standard error of a data set. Standard Error Of The Mean Definition The margin of error and the confidence interval are based on a quantitative measure of uncertainty: the standard error.

Loading... Standard Error Vs Standard Deviation It just happens to be the same thing. All right. And I think you already do have the sense that every trial you take, if you take 100, you're much more likely, when you average those out, to get close to

It doesn't have to be crazy. Difference Between Standard Error And Standard Deviation You can change this preference below. So here, what we're saying is this is the variance of our sample means. Later sections will present the standard error of other statistics, such as the standard error of a proportion, the standard error of the difference of two means, the standard error of

## Standard Error Vs Standard Deviation

T-distributions are slightly different from Gaussian, and vary depending on the size of the sample. http://www.investopedia.com/terms/s/standard-error.asp Because the 9,732 runners are the entire population, 33.88 years is the population mean, μ {\displaystyle \mu } , and 9.27 years is the population standard deviation, σ. Standard Error Formula Population parameter Sample statistic N: Number of observations in the population n: Number of observations in the sample Ni: Number of observations in population i ni: Number of observations in sample Standard Error Regression American Statistical Association. 25 (4): 30–32.

Because of random variation in sampling, the proportion or mean calculated using the sample will usually differ from the true proportion or mean in the entire population. Then you do it again, and you do another trial. So it turns out that the variance of your sampling distribution of your sample mean is equal to the variance of your original distribution-- that guy right there-- divided by n. Edwards Deming. Standard Error Calculator

Now, to show that this is the variance of our sampling distribution of our sample mean, we'll write it right here. Hyattsville, MD: U.S. So 1 over the square root of 5. The sample mean will very rarely be equal to the population mean.

And eventually, we'll approach something that looks something like that. Standard Error Of Proportion But, as you can see, hopefully that'll be pretty satisfying to you, that the variance of the sampling distribution of the sample mean is just going to be equal to the Wolfram Language» Knowledge-based programming for everyone.

## As a result, we need to use a distribution that takes into account that spread of possible σ's.

The standard deviation of the age for the 16 runners is 10.23, which is somewhat greater than the true population standard deviation σ = 9.27 years. National Center for Health Statistics (24). Let's do another 10,000. Standard Error Symbol Show more Loading...

Loading... The unbiased standard error plots as the ρ=0 diagonal line with log-log slope -½. poysermath 552,484 views 9:56 Standard Deviation vs Standard Error - Duration: 3:57. Skip to main contentSubjectsMath by subjectEarly mathArithmeticAlgebraGeometryTrigonometryStatistics & probabilityCalculusDifferential equationsLinear algebraMath for fun and gloryMath by gradeK–2nd3rd4th5th6th7th8thHigh schoolScience & engineeringPhysicsChemistryOrganic ChemistryBiologyHealth & medicineElectrical engineeringCosmology & astronomyComputingComputer programmingComputer scienceHour of CodeComputer animationArts

Loading... This gives 9.27/sqrt(16) = 2.32. The variability of a statistic is measured by its standard deviation. Notice that the population standard deviation of 4.72 years for age at first marriage is about half the standard deviation of 9.27 years for the runners.

and Keeping, E.S. (1963) Mathematics of Statistics, van Nostrand, p. 187 ^ Zwillinger D. (1995), Standard Mathematical Tables and Formulae, Chapman&Hall/CRC. Todd Grande 25,638 views 9:33 z-test vs. See unbiased estimation of standard deviation for further discussion. So I think you know that, in some way, it should be inversely proportional to n.

Or decreasing standard error by a factor of ten requires a hundred times as many observations. Andrew Jahn 13,986 views 5:01 Statistics for Science - Duration: 11:01. And if we did it with an even larger sample size-- let me do that in a different color. JSTOR2682923. ^ Sokal and Rohlf (1981) Biometry: Principles and Practice of Statistics in Biological Research , 2nd ed.

Journal of the Royal Statistical Society. If σ is known, the standard error is calculated using the formula σ x ¯   = σ n {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt {n}}}} where σ is the And of course, the mean-- so this has a mean. Personally, I like to remember this, that the variance is just inversely proportional to n, and then I like to go back to this, because this is very simple in my

Working... National Center for Health Statistics typically does not report an estimated mean if its relative standard error exceeds 30%. (NCHS also typically requires at least 30 observations – if not more


text:
• Biswajoy Brahmachari

Articles written in Pramana – Journal of Physics

• Sterile neutrino in a minimal three-generation see-saw model

We investigate symmetries in Dirac and Majorana mass matrices of neutrinos in a three-generation scenario. We show that if we invokeLe +Lμ-LτxS2R symmetry, one combination of right-handed neutrino states remains massless which can be interpreted as a sterile neutrino. Next we consider a SU2Lx U(1)yx U(l)R gauge model and show how higher-dimensional operators can induce mixing between left- and right-handed states which explains solar, atmospheric and LSND experimental results.

• Working group report: Neutrino and astroparticle physics

This is the report of neutrino and astroparticle physics working group at WHEPP-7. Discussions and work on CP violation in long baseline neutrino experiments, ultra high energy neutrinos, supernova neutrinos and water Cerenkov detectors are discussed.

• Neutrinoless double beta decay with small and hierarchical neutrino mass

We construct a model where neutrino Majorana masses are small and hierarchical but where neutrinoless double beta decay occurs at an observable rate potentially detectable by present day experiments.

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


text:
# Find the code from the image

Find the numerical code from the images.

You don't get any hints.

• Do you mean find what the code is or find the coded message? – William Pennanti May 3 '20 at 19:06
• find what the code is. Sorry for the confusion – Questwalker May 3 '20 at 19:12

I'm a bit confused what you're asking here

The middle tile is the multiple of all the other tiles divided by the digit which there is 3 of.

## Code pattern

To get the number in the middle,

1. multiply all the four numbers orthogonally next to it, then

2. multiply by all the numbers diagonally on the corners, except one which corresponds to the background colour (cyan, magenta, yellow, or black, in the CMYK colour system).

## How it works

First one:

Yellow is bottom left in the CMYK system, so ignore the bottom left number $$4$$ but multiply by all the others. Orthogonally, $$4\times5\times2\times7=280$$. Diagonally, $$2\times7\times4=56$$. Product is $$280\times56=15680$$.

Second one:

Magenta is top right in the CMYK system, but apparently we should actually ignore one of the $$2$$s, not the top right number $$6$$, and multiply by all the others. Orthogonally, $$1\times3\times2\times5=30$$. Diagonally, $$2\times6\times3=36$$. Product is $$30\times36=1080$$.

Third one:

Black is bottom right in the CMYK system, so ignore the bottom right number $$3$$ but multiply by all the others. Orthogonally, $$3\times1\times2\times4=24$$. Diagonally, $$1\times8\times3=24$$. Product is $$24\times24=576$$.

Fourth one:

Cyan is top left in the CMYK system, so ignore the top left number $$1$$ but multiply by all the others. Orthogonally, $$9\times4\times4\times1=144$$. Diagonally, $$1\times2\times3=6$$. Product is $$144\times6=864$$.


text:
×

# Probability Problem

A man tosses a coin $$10$$ times, scoring $$1$$ point for each head and $$2$$ points for each tail. Let $$P(k)$$ be the probability of scoring at least $$k$$ points.

Find the largest value of $$k$$ such that $$P(k)>\frac{1}{2}$$

Note by Krishna Jha
3 years, 10 months ago

Sort by:

We can make use of a generating function to get the number of ways to score points:

$$G(z) = (z^1+z^2)^{10}$$

The coefficient of each $$z^i$$ for i=10..20 is the number of ways of scoring 'i' points.

We can see that the largest k occurs in the middle of the expansion, which is k=15

$$P(k=15) = \dfrac{\sum_{i=5}^{10}\binom{10}{i}}{2^{10}}=\frac{638}{1024}=0.623046875$$ · 3 years, 10 months ago

20 · 1 year, 11 months ago


text:
[ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

# 6. Viewing Cross-References

RefTeX can display cross-referencing information. This means, if two document locations are linked, RefTeX can display the matching location(s) in another window. The \label and \ref macros are one way of establishing such a link. Also, a \cite macro is linked to the corresponding \bibitem macro or a BibTeX database entry.

The feature is invoked by pressing C-c & (reftex-view-crossref) while point is on the key argument of a macro involved in cross-referencing. You can also click with S-mouse-2 on the macro argument. Here is what will happen for individual classes of macros:

\ref

Display the corresponding label definition. All usual variants(7) of the \ref macro are active for cross-reference display. This works also for labels defined in an external document when the current document refers to them through the xr interface (see xr (LaTeX package)).

\label

Display a document location which references this label. Pressing C-c & several times moves through the entire document and finds all locations. Not only the \label macro but also other macros with label arguments (as configured with reftex-label-alist) are active for cross-reference display.

\cite

Display the corresponding BibTeX database entry or \bibitem. All usual variants(8) of the \cite macro are active for cross-reference display.

\bibitem

Display a document location which cites this article. Pressing C-c & several times moves through the entire document and finds all locations.

BibTeX

C-c & is also active in BibTeX buffers. All locations in a document where the database entry at point is cited will be displayed. On first use, RefTeX will prompt for a buffer which belongs to the document you want to search. Subsequent calls will use the same document, until you break this link with a prefix argument to C-c &.

\index

Display other locations in the document which are marked by an index macro with the same key argument. Along with the standard \index and \glossary macros, all macros configured in reftex-index-macros will be recognized.

While the display of cross referencing information for the above mentioned macros is hard-coded, you can configure additional relations in the variable reftex-view-crossref-extra.

 [ < ] [ > ] [ << ] [ Up ] [ >> ] [Top] [Contents] [Index] [ ? ]

This document was generated by Ralf Angeli on August, 9 2009 using texi2html 1.78.