Revisiting the sifting integral: an interesting special case

Order Complexes ◽

Special Case ◽

The Way

We consider the problem of constructing a convex ear decomposition for a poset. The usual technique, introduced by Nyman and Swartz, starts with a $CL$-labeling and uses this to shell the 'ears' of the decomposition. We axiomatize the necessary conditions for this technique as a "$CL$-ced" or "$EL$-ced". We find an $EL$-ced of the $d$-divisible partition lattice, and a closely related convex ear decomposition of the coset lattice of a relatively complemented finite group. Along the way, we construct new $EL$-labelings of both lattices. The convex ear decompositions so constructed are formed by face lattices of hypercubes. We then proceed to show that if two posets $P_{1}$ and $P_{2}$ have convex ear decompositions ($CL$-ceds), then their products $P_{1}\times P_{2}$, $P_{1}\check{\times} P_{2}$, and $P_{1}\hat{\times} P_{2}$ also have convex ear decompositions ($CL$-ceds). An interesting special case is: if $P_{1}$ and $P_{2}$ have polytopal order complexes, then so do their products.

Log canonical pairs with good augmented base loci

Compositio Mathematica ◽

10.1112/s0010437x13007628 ◽

2014 ◽

Vol 150 (4) ◽

pp. 579-592 ◽

Cited By ~ 6

Author(s):

Caucher Birkar ◽

Zhengyu Hu

Keyword(s):

Minimal Model ◽

Surjective Morphism ◽

Normal Variety ◽

Base Locus ◽

Log Canonical ◽

Canonical Pair ◽

Base Loci ◽

AbstractLet $(X,B)$ be a projective log canonical pair such that $B$ is a $\mathbb{Q}$-divisor, and that there is a surjective morphism $f: X\to Z$ onto a normal variety $Z$ satisfying $K_X+B\sim _{\mathbb{Q}} f^*M$ for some big $\mathbb{Q}$-divisor $M$, and the augmented base locus ${\mathbf{B}}_+(M)$ does not contain the image of any log canonical centre of $(X,B)$. We will show that $(X,B)$ has a good log minimal model. An interesting special case is when $f$ is the identity morphism.

Message-Based Web Service Composition, Integrity Constraints, and Planning under Uncertainty: A New Connection

Journal of Artificial Intelligence Research ◽

10.1613/jair.2716 ◽

2009 ◽

Vol 35 ◽

pp. 49-117 ◽

Cited By ~ 27

Author(s):

J. Hoffmann ◽

P. Bertoli ◽

M. Helmert ◽

M. Pistore

Keyword(s):

Web Service ◽

Service Composition ◽

Web Service Composition ◽

Integrity Constraints ◽

Planning Under Uncertainty ◽

Ai Planning ◽

Planning Tools ◽

Service Application ◽

Thanks to recent advances, AI Planning has become the underlying technique for several applications. Figuring prominently among these is automated Web Service Composition (WSC) at the "capability" level, where services are described in terms of preconditions and effects over ontological concepts. A key issue in addressing WSC as planning is that ontologies are not only formal vocabularies; they also axiomatize the possible relationships between concepts. Such axioms correspond to what has been termed "integrity constraints" in the actions and change literature, and applying a web service is essentially a belief update operation. The reasoning required for belief update is known to be harder than reasoning in the ontology itself. The support for belief update is severely limited in current planning tools. Our first contribution consists in identifying an interesting special case of WSC which is both significant and more tractable. The special case, which we term "forward effects", is characterized by the fact that every ramification of a web service application involves at least one new constant generated as output by the web service. We show that, in this setting, the reasoning required for belief update simplifies to standard reasoning in the ontology itself. This relates to, and extends, current notions of "message-based" WSC, where the need for belief update is removed by a strong (often implicit or informal) assumption of "locality" of the individual messages. We clarify the computational properties of the forward effects case, and point out a strong relation to standard notions of planning under uncertainty, suggesting that effective tools for the latter can be successfully adapted to address the former. Furthermore, we identify a significant sub-case, named "strictly forward effects", where an actual compilation into planning under uncertainty exists. This enables us to exploit off-the-shelf planning tools to solve message-based WSC in a general form that involves powerful ontologies, and requires reasoning about partial matches between concepts. We provide empirical evidence that this approach may be quite effective, using Conformant-FF as the underlying planner.

ON THE NUMBER OF REFUSALS IN A BUSY PERIOD

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964899131061 ◽

1999 ◽

Vol 13 (1) ◽

pp. 71-74 ◽

Cited By ~ 8

Author(s):

Erol A. Peköz

Keyword(s):

Service Time ◽

Busy Period ◽

Queueing Systems ◽

Interarrival Time ◽

Direct Argument ◽

The Mean ◽

Formulas are derived for moments of the number of refused customers in a busy period for the M/GI/1/n and the GI/M/1/n queueing systems. As an interesting special case for the M/GI/1/n system, we note that the mean number is 1 when the mean interarrival time equals the mean service time. This provides a more direct argument for a result given in Abramov [1].

New fractional calculus results involving Srivastava’s general class of multivariable polynomials and The H̅ - function

Journal of Applied Mathematics Statistics and Informatics ◽

10.1515/jamsi-2015-0002 ◽

2015 ◽

Vol 11 (1) ◽

pp. 19-32

Author(s):

V. B. L. Chaurasia ◽

Vinod Gill

Keyword(s):

Differential Operator ◽

Fractional Calculus ◽

Wide Class ◽

Mathematical Analysis ◽

Fractional Differential Operator ◽

Fractional Calculus Operators ◽

Fractional Differential ◽

Special Case ◽

Interesting Account

Abstract A significantly large number of earlier works on the subjects of fractional calculus give interesting account of the theory and applications of fractional calculus operators in many different areas of mathematical analysis. In the present paper, we study and develop an important result involving a fractional differential operator for the product of general multivariable polynomials, general polynomial set and two -functions. The result discussed here can be used to investigate a wide class of new and known results, hitherto scattered in the literature. For the sake of illustration, six interesting special case have also been recorded here of our main findings.

Scattering and bound states of spin-0 particles in a nonminimal vector double-step potential

Canadian Journal of Physics ◽

10.1139/p2012-043 ◽

2012 ◽

Vol 90 (5) ◽

pp. 481-486 ◽

Cited By ~ 5

Author(s):

L.P. de Oliveira ◽

A.S. de Castro

Keyword(s):

Incident Wave ◽

Bound States ◽

Bound State ◽

Bound State Solution ◽

Double Step ◽

Step Potential ◽

Transmission Amplitude ◽

Limiting Case ◽

The problem of spin-0 particles subject to a nonminimal vector double-step potential is explored in the context of Duffin–Kemmer–Petiau theory. Surprisingly, one can never have an incident wave totally reflected, and the transmission amplitude has complex poles corresponding to bound states. The interesting special case of bosons embedded in a sign potential with its unique bound-state solution is analyzed as a limiting case.

A KINETIC STUDY OF THE HYDROLYSIS OF BENZALANILINE

Canadian Journal of Chemistry ◽

10.1139/v53-051 ◽

1953 ◽

Vol 31 (4) ◽

pp. 361-376 ◽

Cited By ~ 20

Author(s):

A. V. Willi ◽

R. E. Robertson

Keyword(s):

Kinetic Study ◽

Acid Catalysis ◽

Catalyst Concentration ◽

Effect Of Substituents ◽

General Acid ◽

Acid Catalyzed ◽

Hydrolysis Of ◽

The rates of the acid catalyzed hydrolysis of a series of para substituted benzalanilines have been studied in 50/50 methanol–water in the presence of acetate buffers. Special and general acid catalysis were observed. The effect of para substituents on the rate is different for the charged and uncharged catalyst, and Hammett's relation cannot be applied. Similarly the effect of substituents on the Arrhenius constants for the two cases is different. The para dimethylamino derivative provides an interesting special case. For low buffer concentrations and in unbuffered solutions certain deviations were observed which show that the dependence of the rate on the catalyst concentration is more complicated than the equation[Formula: see text]

Critical Case Stochastic Phylogenetic Tree Model via the Laplace Transform

Demonstratio Mathematica ◽

10.2478/dema-2014-0038 ◽

2014 ◽

Vol 47 (2) ◽

Author(s):

Krzysztof Bartoszek ◽

Michał Krzeminski

Keyword(s):

Laplace Transform ◽

Phylogenetic Trees ◽

Birth Rate ◽

Critical Case ◽

Mathematical Tool ◽

Tree Model ◽

Branching Patterns ◽

The Laplace Transform ◽

AbstractBirth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this, we correct the proof of Liggett and Schinazi (2009) in the critical case.

Double-Dimer Pairings and Skew Young Diagrams

The Electronic Journal of Combinatorics ◽

10.37236/617 ◽

2011 ◽

Vol 18 (1) ◽

Cited By ~ 12

Author(s):

Richard W. Kenyon ◽

David B. Wilson

Keyword(s):

Bipartite Graph ◽

Perfect Matching ◽

Outer Face ◽

Young Diagrams ◽

Grid Spacing ◽

Dimer Model ◽

Dyck Paths ◽

We study the number of tilings of skew Young diagrams by ribbon tiles shaped like Dyck paths, in which the tiles are "vertically decreasing". We use these quantities to compute pairing probabilities in the double-dimer model: Given a planar bipartite graph $G$ with special vertices, called nodes, on the outer face, the double-dimer model is formed by the superposition of a uniformly random dimer configuration (perfect matching) of $G$ together with a random dimer configuration of the graph formed from $G$ by deleting the nodes. The double-dimer configuration consists of loops, doubled edges, and chains that start and end at the boundary nodes. We are interested in how the chains connect the nodes. An interesting special case is when the graph is $\varepsilon(\mathbb Z\times\mathbb N)$ and the nodes are at evenly spaced locations on the boundary $\mathbb R$ as the grid spacing $\varepsilon\to0$.

The spectra of Fredholm operators in locally convex spaces

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100038275 ◽

1964 ◽

Vol 60 (4) ◽

pp. 801-806 ◽

Cited By ~ 2

Author(s):

P. A. Olagunju ◽

T. T. West

Keyword(s):

Sufficient Conditions ◽

Trace Class ◽

Locally Convex Space ◽

Fredholm Operators ◽

Negative Real Axis ◽

Necessary And Sufficient ◽

Locally Convex ◽

Special Case ◽

General Banach Space

1. Notation and definitions. In this paper necessary and sufficient conditions are found for the spectrum of a Fredholm operator in a locally convex space (always taken to be Hausdorff) to lie on the non-negative real axis of the complex plane. Some results of Grothendieck(2) allow us to obtain the results in this general form; an interesting special case is the trace-class of operators in a general Banach space. We also deal with the case of Hilbert–Schmidt operators in a Hilbert space.