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

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

doi:10.1016/s0038-1098(98)00458-x
fatcat:uio3rax46nbarknp53gk3pa2tu
*idempotency*... of*idempotency*) will therefore be more efficient. ... We note that the first derivative of the functional is undefined for*idempotent*DMs. ...##
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Bifurcations and exceptional points in a ${ \mathcal P }{ \mathcal T }$-symmetric dipolar Bose–Einstein condensate

2016
*
Journal of Physics A: Mathematical and Theoretical
*

Representation of bicomplex numbers in the

doi:10.1088/1751-8113/49/48/485301
fatcat:rfof3bldejbvdczk34psgxpq2i
*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. ...##
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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*...##
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An adaptive test sequences generation method for the users needs
[chapter]

1996
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Protocol Test Systems VIII
*

is also an

doi:10.1007/978-0-387-34988-6_7
fatcat:fcgk6nqhpzb45b4pritbfnwi74
*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 ...##
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SOS rule formats for idempotent terms and idempotent unary operators

2014
*
The Journal of Logic and Algebraic Programming
*

A unary operator f is

doi:10.1016/j.jlap.2013.07.003
fatcat:ipt6w2ne65ddfnjahcoqoldx3m
*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*...##
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Identification of general and double aggregation operators using monotone smoothing

2005
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European Society for Fuzzy Logic and Technology
*

Besides monotonicity, there could be other restrictions, such as commutativity,

dblp:conf/eusflat/BeliakovC05
fatcat:c6lnq5u6t5czfpmvvlvgyqzili
*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 ...##
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SOS Rule Formats for Idempotent Terms and Idempotent Unary Operators
[chapter]

2013
*
Lecture Notes in Computer Science
*

A unary operator f is

doi:10.1007/978-3-642-35843-2_11
fatcat:q2s4qmcwsfdbfmvajxkdshr654
*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*...##
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Density matrices in O(N) electronic structure calculations: theory and applications
[article]

1998
*
arXiv
*
pre-print

We note that in such methods a crucially important constraint is that the density matrix must be

arXiv:cond-mat/9810042v2
fatcat:mrrwtytknba3fpkaflqwwa3miu
*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. ...##
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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. ...##
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A Formulation of the Potential for Communication Condition using C2KA

2014
*
Electronic Proceedings in Theoretical Computer Science
*

We say that a semiring is

doi:10.4204/eptcs.161.15
fatcat:ondny4ofjrbjrcfrlbvoz6ljea
*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*. ...##
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ON MAXIMAL SUBGROUPS OF IDEMPOTENT-GENERATED SEMIGROUPS ASSOCIATED WITH BIORDERED SETS

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

doi:10.1017/s0004972721001052
fatcat:lbhmv5kuibclhezc4y5ta4yswi
*idempotents*play in determining the structure or*behaviour*of an algebra ... of their semilattices of*idempotents*. ...##
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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*. ...##
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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. ...##
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Stochastic monotonicity and the Markov product for copulas
[article]

2020
*
arXiv
*
pre-print

Applying the latter result, we identify all

arXiv:2012.08324v1
fatcat:3lj6zmovobcrzafhrpzjip2xru
*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. ...##
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Deriving Syntax and Axioms for Quantitative Regular Behaviours
[chapter]

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

doi:10.1007/978-3-642-04081-8_11
fatcat:wtaet2qotfasldbqr6capj2hku
*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. ...
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