scholarly journals The extra-nice dimensions

2021 ◽  
Author(s):  
R. Oset Sinha ◽  
M. A. S. Ruas ◽  
R. Wik Atique
Keyword(s):  
One Dimension ◽  
Sufficient Condition ◽  
Stable Maps ◽  
Hyperplane Sections

AbstractWe define the extra-nice dimensions and prove that the subset of locally stable 1-parameter families in $$C^{\infty }(N\times [0,1],P)$$ C ∞ ( N × [ 0 , 1 ] , P ) is dense if and only if the pair of dimensions $$(\dim N, \dim P)$$ ( dim N , dim P ) is in the extra-nice dimensions. This result is parallel to Mather’s characterization of the nice dimensions as the pairs (n, p) for which stable maps are dense. The extra-nice dimensions are characterized by the property that discriminants of stable germs in one dimension higher have $${\mathscr {A}}_e$$ A e -codimension 1 hyperplane sections. They are also related to the simplicity of $${\mathscr {A}}_e$$ A e -codimension 2 germs. We give a sufficient condition for any $${\mathscr {A}}_e$$ A e -codimension 2 germ to be simple and give an example of a corank 2 codimension 2 germ in the nice dimensions which is not simple. Then we establish the boundary of the extra-nice dimensions. Finally we answer a question posed by Wall about the codimension of non-simple maps.

On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution

1977 ◽  
Vol 82 (2) ◽  
pp. 297-300 ◽  
Author(s):  
A. V. Godambe
Keyword(s):  
Gamma Distribution ◽  
Exponential Type ◽  
Similar Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Poisson Mixture ◽  
Mixing Distribution ◽  
Poisson Mixtures ◽  
Necessary And Sufficient

AbstractA necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.

A characterization of the Poisson process

1974 ◽  
Vol 11 (1) ◽  
pp. 72-85 ◽  
Author(s):  
S. M. Samuels
Keyword(s):  
Poisson Process ◽  
Renewal Process ◽  
Poisson Processes ◽  
Renewal Processes ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complete Proof ◽  
Necessary And Sufficient

Theorem: A necessary and sufficient condition for the superposition of two ordinary renewal processes to again be a renewal process is that they be Poisson processes.A complete proof of this theorem is given; also it is shown how the theorem follows from the corresponding one for the superposition of two stationary renewal processes.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

scholarly journals Two examples related to conical energies

2022 ◽  
Vol 47 (1) ◽  
pp. 261-281
Author(s):  
Damian Dąbrowski
Keyword(s):  
Singular Integral ◽  
Recent Article ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
The Other ◽  
Independent Interest ◽  
Sufficient Condition ◽  
Lipschitz Graphs ◽  
Big Pieces

In a recent article (2021) we introduced and studied conical energies. We used them to prove three results: a characterization of rectifiable measures, a characterization of sets with big pieces of Lipschitz graphs, and a sufficient condition for boundedness of nice singular integral operators. In this note we give two examples related to sharpness of these results. One of them is due to Joyce and Mörters (2000), the other is new and could be of independent interest as an example of a relatively ugly set containing big pieces of Lipschitz graphs.

A study of enhanced power graphs of finite groups

2019 ◽  
Vol 19 (04) ◽  
pp. 2050062 ◽  
Author(s):  
Samir Zahirović ◽  
Ivica Bošnjak ◽  
Rozália Madarász
Keyword(s):  
Finite Groups ◽  
Prime Power ◽  
Cyclic Subgroup ◽  
Nilpotent Groups ◽  
Sufficient Condition ◽  
Finite Abelian Groups ◽  
Power Graph ◽  
Vertex Set ◽  
A Finite Group

The enhanced power graph [Formula: see text] of a group [Formula: see text] is the graph with vertex set [Formula: see text] such that two vertices [Formula: see text] and [Formula: see text] are adjacent if they are contained in the same cyclic subgroup. We prove that finite groups with isomorphic enhanced power graphs have isomorphic directed power graphs. We show that any isomorphism between undirected power graph of finite groups is an isomorphism between enhanced power graphs of these groups, and we find all finite groups [Formula: see text] for which [Formula: see text] is abelian, all finite groups [Formula: see text] with [Formula: see text] being prime power, and all finite groups [Formula: see text] with [Formula: see text] being square-free. Also, we describe enhanced power graphs of finite abelian groups. Finally, we give a characterization of finite nilpotent groups whose enhanced power graphs are perfect, and we present a sufficient condition for a finite group to have weakly perfect enhanced power graph.

Characterization of allergen extracts by two-dimensional electrophoretic techniques: Micropolyspora faeni antigens.

1982 ◽  
Vol 28 (4) ◽  
pp. 993-997 ◽  
Author(s):  
O Vesterberg ◽  
K Holmberg
Keyword(s):  
Isoelectric Focusing ◽  
One Dimension ◽  
Protein Antigens ◽  
Thermophilic Actinomycetes ◽  
Saprobic Fungi ◽  
Increased Sensitivity ◽  
Electrophoretic Techniques ◽  
Protein Components ◽  
Allergen Extracts

Abstract Thermophilic actinomycetes and saprobic fungi are important in the etiology of allergic occupational diseases such as "farmer's lung" disease. Each such organism produces several protein antigens. Inhaled, these antigens stimulate production of antibodies. Detection of precipitating antibodies has been useful in the diagnosis of diseases so induced. Characterization of allergen extracts from microorganisms associated with these diseases is important, to improve the sensitivity and precision of the precipitin analysis. For this purpose we submitted crude allergen extracts to electrophoresis and isoelectric focusing in agarose gels. Staining the gels revealed many protein components in each extract, especially after isoelectric focusing. After separation in one dimension, a lane of gel was cut out and the proteins were electrophoresed at right angles into another gel, which contained antibodies. Several arcs of immunoprecipitates, indicating different antigens, were seen. This technique ("crossed immunoelectrofocusing") has earlier been used with polyacrylamide in the first dimension, but it is improved by using instead agarose of a special quality. Further to improve the quantification, we isolated pieces of gel containing the proteins of interest and used them as samples in zone immunoelectrophoresis assay. This method is straightforward, easy to evaluate, and about 100-fold as sensitive as radial immunodiffusion. The amount of protein in each sample is usually proportional to the distance from the upper gel surface to the front of each immunoprecipitate. The increased sensitivity allows study of many hitherto unexamined antigens.

The Effective Cone of the Kontsevich Moduli Space

2008 ◽  
Vol 51 (4) ◽  
pp. 519-534 ◽  
Author(s):  
Izzet Coskun ◽  
Joe Harris ◽  
Jason Starr
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Complete Characterization ◽  
Stable Maps ◽  
Linear Combinations ◽  
Effective Divisors ◽  
Effective Cone

AbstractIn this paper we prove that the cone of effective divisors on the Kontsevich moduli spaces of stable maps, , stabilize when r ≥ d. We give a complete characterization of the effective divisors on . They are non-negative linear combinations of boundary divisors and the divisor of maps with degenerate image.

On weak convergence within the hnbue family of life distributions

1984 ◽  
Vol 21 (03) ◽  
pp. 654-660 ◽  
Author(s):  
Sujit K. Basu ◽  
Manish C. Bhattacharjee
Keyword(s):  
Weak Convergence ◽  
Exponential Distribution ◽  
Limiting Distribution ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moment Sequence ◽  
Positive Order ◽  
Life Distributions ◽  
Necessary And Sufficient

We show that the HNBUE family of life distributions is closed under weak convergence and that weak convergence within this family is equivalent to convergence of each moment sequence of positive order to the corresponding moment of the limiting distribution. A necessary and sufficient condition for weak convergence to the exponential distribution is given, based on a new characterization of exponentials within the HNBUE family of life distributions.

scholarly journals Formal Modeling and Analysis of Fairness Characterization of E-Commerce Protocols

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Chengwei Zhang ◽  
Xiaohong Li ◽  
Jing Hu ◽  
Zhiyong Feng ◽  
Jiaojiao Song
Keyword(s):  
Formal Modeling ◽  
Sufficient Condition ◽  
Formal Approach ◽  
Common Assumption ◽  
Modeling And Analysis ◽  
Verification Method ◽  
Space Model ◽  
The Past

In the past, fairness verification of exchanges between the traders in E-commerce was based on a common assumption, so-called nonrepudiation property, which says that if the parties involved can deny that they have received or sent some information, then the exchanging protocol is unfair. So, the nonrepudiation property is not a sufficient condition. In this paper, we formulate a new notion of fairness verification based on the strand space model and propose a method for fairness verification, which can potentially determine whether evidences have been forged in transactions. We first present an innovative formal approach not to depend on nonrepudiation, and then establish a relative trader model and extend the strand space model in accordance with traders’ behaviors of E-commerce. We present a case study to demonstrate the effectiveness of our verification method.

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