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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
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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
2016
Journal of Physics A: Mathematical and Theoretical
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2016 pre-print arXiv:1605.01927v1 fatcat:hoz66yix7fdbffhpof2tl4srcuOther Versions
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
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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]
1996
Protocol Test Systems VIII
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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
2014
The Journal of Logic and Algebraic Programming
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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
2005
European Society for Fuzzy Logic and Technology
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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]
2013
Lecture Notes in Computer Science
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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]
1998
arXiv
pre-print
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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
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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
2014
Electronic Proceedings in Theoretical Computer Science
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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
2022
Bulletin of the Australian Mathematical Society
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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
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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
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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]
2020
arXiv
pre-print
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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]
2009
Lecture Notes in Computer Science
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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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