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Failure of density-matrix minimization methods for linear-scaling density-functional theory using the Kohn penalty-functional

P.D. Haynes, M.C. Payne
1998 Solid State Communications  
for performing linear-scaling calculations within density-functional theory by direct minimization with respect to the single-particle density-matrix using a penalty-functional to exactly enforce the idempotency  ...  of idempotency) will therefore be more efficient.  ...  We note that the first derivative of the functional is undefined for idempotent DMs.  ... 
doi:10.1016/s0038-1098(98)00458-x fatcat:uio3rax46nbarknp53gk3pa2tu

Bifurcations and exceptional points in a ${ \mathcal P }{ \mathcal T }$-symmetric dipolar Bose–Einstein condensate

Robin Gutöhrlein, Holger Cartarius, Jörg Main, Günter Wunner
2016 Journal of Physics A: Mathematical and Theoretical  
Representation of bicomplex numbers in the idempotent basis There exists a representation of bicomplex numbers in an idempotent basis.  ...  We can now consider the implication the idempotent properties have on the basic arithmetic operations.  ... 
doi:10.1088/1751-8113/49/48/485301 fatcat:rfof3bldejbvdczk34psgxpq2i

Page 3158 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
The fact that the group Aut(B) of biholomorphic automorphisms of the ball B acts transitively on B also plays an important role, as it permits the author to analyse the behaviour of the idempotent f (and  ...  If f:B — B, f #0, is an idempotent such that f(0) =0, then its Fréchet derivative P = f'(0) is a projection (a linear idempotent) with ||P|| = 1 that plays a decisive role in the study of both the idempotent  ... 

An adaptive test sequences generation method for the users needs [chapter]

Richard Castanet, Christophe Chevrier, Ousmane Koné, Bertrand Le Saëc
1996 Protocol Test Systems VIII  
is also an idempotent.  ...  In monoid theory, this notion can be found in the notion of idempotence: f E M is an idempotent if f 0 f = f2 = f The neutral element of a monoid is always an idempotent and if the monoid has a zero, it  ...  DR Figure 6 10SM for the initiator part of the 1nRes protocol ICOlreq • Test purpose: Behaviour with respect to connection timer -this test aims at verifying the connection protocol with respect to  ... 
doi:10.1007/978-0-387-34988-6_7 fatcat:fcgk6nqhpzb45b4pritbfnwi74

SOS rule formats for idempotent terms and idempotent unary operators

Luca Aceto, Anna Ingolfsdottir, Eugen-Ioan Goriac
2014 The Journal of Logic and Algebraic Programming  
A unary operator f is idempotent if the equation f (x) = f (f (x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator if a = a a.  ...  The proposed rule format relies on a companion one ensuring that certain terms are idempotent with respect to some binary operator.  ...  Terms built using operators from the signature of a TSS are usually considered modulo some notion of behavioural equivalence, which is used to indicate when two terms describe 'essentially the same behaviour  ... 
doi:10.1016/j.jlap.2013.07.003 fatcat:ipt6w2ne65ddfnjahcoqoldx3m

Identification of general and double aggregation operators using monotone smoothing

Gleb Beliakov, Tomasa Calvo
2005 European Society for Fuzzy Logic and Technology  
Besides monotonicity, there could be other restrictions, such as commutativity, idempotency, or disjunctive/conjunctive behaviour.  ...  (a) G, H are conjunctive, F is idempotent; (b) G, H are disjunctive, F is idempotent; (c) G, H are idempotent, F is conjunctive; (d) G, H are idempotent, F is disjunctive; (e) G is idempotent, F, H are  ... 
dblp:conf/eusflat/BeliakovC05 fatcat:c6lnq5u6t5czfpmvvlvgyqzili

SOS Rule Formats for Idempotent Terms and Idempotent Unary Operators [chapter]

Luca Aceto, Eugen-Ioan Goriac, Anna Ingólfsdóttir
2013 Lecture Notes in Computer Science  
A unary operator f is idempotent if the equation f (x) = f (f (x)) holds. On the other end, an element a of an algebra is said to be an idempotent for a binary operator if a = a a.  ...  The proposed rule format relies on a companion one ensuring that certain terms are idempotent with respect to some binary operator.  ...  Terms built using operators from the signature of a TSS are usually considered modulo some notion of behavioural equivalence, which is used to indicate when two terms describe 'essentially the same behaviour  ... 
doi:10.1007/978-3-642-35843-2_11 fatcat:q2s4qmcwsfdbfmvajxkdshr654

Density matrices in O(N) electronic structure calculations: theory and applications [article]

D.R.Bowler, M.J.Gillan
1998 arXiv   pre-print
We note that in such methods a crucially important constraint is that the density matrix must be idempotent (i.e. its eigenvalues must all be zero or unity).  ...  Indeed, it is one of the standard methods of achieving linear-scaling behaviour in tight-binding calculations 23 .  ...  So once again the variational behaviour given by LNV is essential, just as it is for calculating forces -and for basically the same reason.  ... 
arXiv:cond-mat/9810042v2 fatcat:mrrwtytknba3fpkaflqwwa3miu

Page 4352 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
For finite semigroups, x® denotes the unique power of x that is idempotent.  ...  We formulate the discipline of uniform receptiveness by means of a type system, and then we study its impact on behavioural equivalences and process reasoning.  ... 

A Formulation of the Potential for Communication Condition using C2KA

Jason Jaskolka, Ridha Khedri
2014 Electronic Proceedings in Theoretical Computer Science  
We say that a semiring is idempotent if operator + is idempotent. Every idempotent semiring has a natural partial order ≤ on S defined by a ≤ b ⇐⇒ a+b = b.  ...  A monoid is called commutative if · is commutative and a monoid is called idempotent if · is idempotent.  ... 
doi:10.4204/eptcs.161.15 fatcat:ondny4ofjrbjrcfrlbvoz6ljea

ON MAXIMAL SUBGROUPS OF IDEMPOTENT-GENERATED SEMIGROUPS ASSOCIATED WITH BIORDERED SETS

SEAN GARDINER
2022 Bulletin of the Australian Mathematical Society  
It is a long-standing theme of great interest to algebraists, and semigroup theorists in particular, to understand the role that idempotents play in determining the structure or behaviour of an algebra  ...  of their semilattices of idempotents.  ... 
doi:10.1017/s0004972721001052 fatcat:lbhmv5kuibclhezc4y5ta4yswi

Page 2535 of Mathematical Reviews Vol. , Issue 2000d [page]

2000 Mathematical Reviews  
For the matrix algebra, the present authors show that, conversely, this behaviour actually characterizes the idempotents.  ...  Soc. (2) 23 (1981), no. 1, 171-178; MR 83d:46056] have shown the linear behaviour of the spectral radius near idempotents.  ... 

Page 8317 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
The behaviour of this class of algebras has been studied in several papers and when 2y # | the existence of an idempotent and the associated Peirce decomposition is well known.  ...  In this case, products of elements in U and V have a much better behaviour than in the general case of second-order Bernstein algebras.  ... 

Stochastic monotonicity and the Markov product for copulas [article]

Karl Friedrich Siburg, Christopher Strothmann
2020 arXiv   pre-print
Applying the latter result, we identify all idempotent stochastically monotone copulas as ordinal sums of the independence copula Π.  ...  Ordinal sums of Π are the only idempotent 2-copulas which are stochastically increasing. Proof. The proof treats three distinct cases, depending on the behaviour along the diagonal.  ...  Let C be an idempotent 2-copula.  ... 
arXiv:2012.08324v1 fatcat:3lj6zmovobcrzafhrpzjip2xru

Deriving Syntax and Axioms for Quantitative Regular Behaviours [chapter]

Filippo Bonchi, Marcello Bonsangue, Jan Rutten, Alexandra Silva
2009 Lecture Notes in Computer Science  
In previous work, we applied a similar approach to a class of systems (without weights) that generalizes both the results of Kleene (on rational languages and DFA's) and Milner (on regular behaviours and  ...  This is problematic because idempotency played a crucial role in our previous results to ensure that expressions denote finite-state behaviours.  ...  and non-idempotent sums.  ... 
doi:10.1007/978-3-642-04081-8_11 fatcat:wtaet2qotfasldbqr6capj2hku
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