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41.
Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation. 相似文献
42.
Laurent Serlet 《Journal of Theoretical Probability》1996,9(3):561-578
We study super-Brownian motion inR
d
starting from a nontrivial finite measure and conditioned to nonextinction as defined by Evans. If (Y
t
)
t0
denotes this process, we provide a new approach to the immortal particle representation of (Y
t
)
t0
. We then show that the measureZ onR
d
defined byZ(B)=
o
1
Y
t
(B) dt is almost surely finite on compact sets whend5 and almost surely infinite on every ball whend4. 相似文献
43.
If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk
n
wherek
n+1
ck
n
then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG). 相似文献
44.
Yu Chen 《Transactions of the American Mathematical Society》1996,348(9):3733-3743
We demonstrate a one to one correspondence between the irreducible projective representations of an affine Kac-Moody group and those of the related loop group, which leads to the results that every non-trivial representation of an affine Kac-Moody group must have its degree greater than or equal to the rank of the group and that the equivalence appears if and only if the group is of type for some . Moreover the characteristics of the base fields for the non-trivial representations are found being always zero.
45.
Michael O'Carroll 《Journal of statistical physics》1993,71(3-4):415-423
We obtain a resolution of the identity operator, for functions on a latticeZ
d, which is derived from the block renormalization group. We use eigenfunctions of the terms of the decomposition to form a basis forl
2(Zd) and show how the basis is generated from lattice wavelets. The lattice spacing is taken to zero and continuum wavelets are obtained. 相似文献
46.
Weiping Wang Bo Liao Tianming Wang Wen Zhu 《International journal of quantum chemistry》2006,106(9):1998-2005
A 3D graphical representation of DNA sequences, which has no circuit or degeneracy, is derived for mathematical denotation of DNA sequence. Based on this graphical representation, we propose a new sequence distance measure. We make use of the corresponding similarity matrix to construct a phylogenic tree by virtue of the fuzzy theory. The examination of phylogenic tree belong to eight species illustrates the utility of our approach. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 相似文献
47.
New 2D graphical representation of DNA sequences 总被引:5,自引:0,他引:5
We consider a 2D graphical representations of DNA sequences, which avoids loss of information associated with crossing and overlapping of the corresponding curve. We outline an approach, which is based on the construction of a three-component vector whose components are the normalized leading eigenvalues of the L/L matrices associated with DNA. The examination of similarities/dissimilarities among the coding sequences of the first exon of beta-globin gene of different species illustrates the utility of the approach. 相似文献
48.
Shinsaku Fujita 《Journal of mathematical chemistry》2007,42(2):215-263
The concepts of double coset representations and sphericities of double cosets are proposed to characterize stereoisomerism, where double cosets are classified into three types, i.e., homospheric double cosets, enantiospheric double cosets, or hemispheric double cosets. They determine modes of substitutions (i.e., chirality fittingness), where homospheric double cosets permit
achiral ligands only; enantiospheric ones permit achiral ligands or enantiomeric pairs; and hemispheric ones permit achiral
and chiral ligands. The sphericities of double cosets are linked to the sphericities of cycles which are ascribed to right
coset representations. Thus, each cycle is assigned to the corresponding sphericity index (a
d
, c
d
, or b
d
) so as to construct a cycle indices with chirality fittingness (CI-CFs). The resulting CI-CFs are proved to be identical
with CI-CFs introduced in Fujita’s proligand method (S. Fujita, Theor. Chem. Acc. 113 (2005) 73–79 and 80–86). The versatility
of the CI-CFs in combinatorial enumeration of stereoisomers is demonstrated by using methane derivatives as examples, where
the numbers of achiral plus chiral stereoisomers, those of achiral stereoisomers, and those of chiral stereoisomers are calculated
separately by means of respective generating functions. 相似文献
49.
Shinsaku Fujita 《Theoretical chemistry accounts》1990,78(1):45-63
Summary A coset representation (G(/G
i
)), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG
i
, is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G
i
) orbit belongs to theG
i
site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions. 相似文献
50.
Christian Borgs Roman Kotecký Salvador Miracle-Solé 《Journal of statistical physics》1991,62(3-4):529-551
Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by
m
(L)=(Inq/E)L
–d
+O(L
–2d
) with respect to the infinite-volume transition point
t
. We also propose an alternative definition of the finite-volume transition temperature
t
(L) which might be useful for numerical calculations because it differs only by exponentially small corrections from
t
. 相似文献