45,777 research outputs found
CM defect and Hilbert function of monomial curves
No full textIn this article we consider a semigroup ring R = K[[Γ ]] of a numerical semigroup Γ
and study the Cohen–Macaulayness of the associated graded ring G(Γ ) := grm(R) :=
⊕n∈N mn/mn+1 and the behaviour of the Hilbert function HR of R.Wedefine a certain (finite)
subset B(Γ ) ⊆ Γ and prove that G(Γ ) is Cohen–Macaulay if and only if B(Γ ) = ∅.
Therefore the subset B(Γ ) is called the Cohen–Macaulay defect of G(Γ ). Further, we prove
that if the degree sequence of elements of the standard basis of Γ is non-decreasing,
then B(Γ ) = ∅ and hence G(Γ ) is Cohen–Macaulay. We consider a class of numerical
semigroups Γ =
Σ3
i=0 Nmi generated by 4 elements m0,m1,m2,m3 such that m1 +m2 =
m0+m3—so called ‘‘balanced semigroups’’. We study the structure of the Cohen–Macaulay
defect B(Γ ) of Γ and particularly we give an estimate on the cardinality |B(Γ , r)| for
every r ∈ N. We use these estimates to prove that the Hilbert function of R is nondecreasing.
Further, we prove that every balanced ‘‘unitary’’ semigroup Γ is ‘‘2-good’’ and
is not ‘‘1-good’’, in particular, in this case, G(Γ ) is not Cohen–Macaulay. We consider a
certain special subclass of balanced semigroups Γ . For this subclass we try to determine
the Cohen–Macaulay defect B(Γ ) using the explicit description of the standard basis of Γ ;
in particular, we prove that these balanced semigroups are 2-good and determine when
exactly G(Γ ) is Cohen–Macaulay
On the Cohen–Macaulayness of some graded rings
No full textLet (R,m) be a 1-dimensional Cohen-Macaulay local ring of multiplicity e and embedding dimension v ≥2 . Let B denote the blowing-up of R along m and let I be the conductor of R in B. Let x be a superficial element in m of degree 1 and I' = (I +xR)/xR . We assume that the length l(I') = 1 . This class of local rings contains the class of 1-dimensional Gorenstein local rings . In section 1, we prove that if the associated graded ring G = gr(R) is Cohen-Macaulay, then I is contained in m^s + xR , where s is the degree of the h-polynomial h(R) of R. In section 2, we give necessary and sufficient conditions for the Cohen-Macaulayness of G.
These conditions are numerical conditions on the h-polynomial h(R) , particularly on its coefficients and the degree in comparison with the difference e − v . In section 3, we give some conditions for the Gorensteinness of G. In section 4, we give a characterisation (see 4.3) of numerical semigroup rings which satisfy the condition l(I') =
Parimal G. Patil, Against a Hindu God: Buddhist philosophy of religion in India
No full textL’ouvrage de P. G. Patil (PGP) est d’une richesse considérable en termes philosophique, philologique et exégétique et restera sans doute une référence pour tous ceux qui s’intéressent à la philosophie indienne bouddhique tardive, et notamment à son versant épistémologique. Il apporte une double contribution à l’étude des textes bouddhiques. D’une part, il est un exemple à suivre dans la méthode d’approche rigoureuse des textes par ses nombreuses références et citations de textes primaires, à ..
Parimal G. Patil, Against a Hindu God: Buddhist philosophy of religion in India
No full textL’ouvrage de P. G. Patil (PGP) est d’une richesse considérable en termes philosophique, philologique et exégétique et restera sans doute une référence pour tous ceux qui s’intéressent à la philosophie indienne bouddhique tardive, et notamment à son versant épistémologique. Il apporte une double contribution à l’étude des textes bouddhiques. D’une part, il est un exemple à suivre dans la méthode d’approche rigoureuse des textes par ses nombreuses références et citations de textes primaires, à ..
BiVO<sub>4</sub> Fern Architectures: A Competitive Anode for Lithium-Ion Batteries
No full textThe development of high‐performance anode materials for lithium‐ion batteries (LIBs) is currently subject to much interest. In this study, BiVO₄ fern architectures are introduced as a new anode material for LIBs. The BiVO₄ fern shows an excellent reversible capacity of 769 mAh g⁻¹ (ultrahigh volumetric capacity of 3984 mAh cm⁻³) at 0.12 A g⁻¹ with large capacity retention. A LIB full cell is then assembled with a BiVO₄ fern anode and LiFePO₄ (LFP, commercial) as cathode material. The device can achieve a capacity of 140 mAh g⁻¹ at 1C rate, that is, 81 % of the capacity of the cathode and maintained to 104 mAh g⁻¹ at a high rate of 8C, which makes BiVO₄ a promising candidate as a high‐energy anode material for LIBs.Deepak P. Dubal, Deepak R. Patil, Santosh S. Patil, N.R. Munirathnam, and Pedro Gomez-Romer
Ecological Applications of Generalized Linear Models and Quasi-likelihood Methods: an Overview
No full textAssessment of Aquatic System Toxicity Using Generalized Linear Models and Quasi-likelihood Techniques
No full textResource management with X.509 inter-domain authorization certificates (InterAC)
No full textCollaboration among independent administrative domains would require: i) confidentiality, integrity, non-repudiation of communication between the domains; ii) minimum and reversible modifications to the intra-domain pre-collaboration setup; iii) maintain functional autonomy while collaborating; and, iv) ability to quickly transform from post-collaboration to pre-collaboration stage. In this paper, we put forward our mechanism that satisfies above requirements while staying within industry standards so that the mechanism becomes practical and deployable. Our approach is based on X.509 certificate extension. We have designed a non-critical extension capturing users' rights in such a unique way that the need for collaboration or the post-collaboration stage does not require update of the certificate. Thus, greatly reducing the revocation costs and size of CRLs. Furthermore, rights amplification and degradation of users from collaborating domains into host domain can be easily performed. Thus, providing functional autonomy to collaborators. Initiation of collaboration among two domains require issuance of one certificate from each domain and revocation of these certificates ends the collaboration - ease of manageability. © 2010 Springer-Verlag
Statistical selection of perimeter-area models for patch mosaics in multiscale landscape analysis
No full textThis paper presents a statistical method for detecting distinct scales of pattern for mosaics of irregular patches, by means of perimeter-area relationships. Krummel et al. (1987) were the first to develop a method for detecting different scaling domains in a landscape of irregular patches, but this method requires investigator judgment and is not completely satisfying. Grossi et al. (2001) suggested a modification of Krummel’s method in order to detect objectively the change points between different scaling domains. Their procedure is based on the selection of the best piecewise linear regression model using a set of statistical tests. Even though the change points were estimated, the null distribution used for testing purposes were those appropriate for known change points. The present paper investigates the effect that estimating the change points has on the underlying distribution theory. The procedure we suggest is based on the selection of the best piecewise linear regression model using a likelihood ratio (LR) test. Each segment of the piecewise linear model corresponds to fractal domain. Breakpoints between different segments are unknown, so the piecewise linear models are non-linear. In this case, the frequency distribution of the LR statistic cannot be approximated by a chi-squared distribution. Instead, Monte Carlo simulation is used to obtain an empirical null distribution of the LR statistic. The suggested method is applied to three patch types (CORINE biotopes) located in the Val Baganza watershed of Italy
Betti Numbers, Grobner Basis And Syzygies For Certain Affine Monomial Curves
No full textLet e > 3 and mo,... ,me_i be positive integers with gcd(m0,... ,me_i) = 1, which form an almost arithmetic sequence, i.e., some e - 1 of these form an arithmetic progression. We further assume that m0,... ,mc_1 generate F := Σ e-1 I=0 Nmi minimally. Note that any three integers and also any arithmetic progression form an almost arithmetic sequence.
We assume that 0 , Y,T be indeterminates. Let p denote the kernel of the if-algebra homomorphism η: K[XQ, ..., XV) Y) -* K^T], defined by r){Xi) = Tm\.. .η{Xp) = Tmp, η](Y) = Tn. Then, p is the defining ideal for the affine monomial curve C in A^, defined parametrically by Xo = Trr^)...)Xv = T^}Y = T*. Furthermore, p is a homogeneous ideal with respect to the gradation on K[X0)... ,XP,F], given by wt(Z0) = mo, • • •, wt(Xp) = mp, wt(Y) = n. Let 4 := K[XQ> ...,XP) Y)/p denote the coordinate ring of C.
With the assumption ch(K) = 0, in Chapter 1 we have derived an explicit formula for μ(DerK(A)), the minimal number of generators for the A-module DerK(A), the derivation module of A. Furthermore, since type(A) = μ(DerK(A)) — 1 and the last Betti number of A is equal to type(A), we therefore obtain an explicit formula for the last Betti number of A as well
A minimal set of binomial generatorsG for the ideal p had been explicitly constructed by PatiL In Chapter 2, we show that the set G is a Grobner basis with respect to grevlex monomial ordering on K[X0)..., Xp, Y]. As an application of this observation, in Chapter 3 we obtain an explicit minimal free resolution for affine monomial curves in A4K defined by four coprime positive integers mo,.. m3, which form a minimal arithmetic progression.
(Please refer the pdf file forformulas
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