How to Go beyond the Case hlin(φ‎) ≥ 5

2016 ◽  
Author(s):  
Isroil A. Ikromov ◽  
Detlef Müller
Keyword(s):  
Lower Bounds ◽  
The Other ◽  
Complex Interpolation ◽  
Restriction Theorem ◽  
Fourier Restriction

This chapter mostly considers the domains of type Dsubscript (l), which are in some sense “closest” to the principal root jet, since it turns out that the other domains Dsubscript (l) with l ≥ 2 are easier to handle. In a first step, by means of some lower bounds on the r-height, this chapter establishes favorable restriction estimates in most situations, with the exception of certain cases where m = 2 and B = 3 or B = 4. In some cases the chapter applies interpolation arguments in order to capture the endpoint estimates for p = psubscript c. Sometimes this can be achieved by means of a variant of the Fourier restriction theorem. However, in most of these cases the chapter applies complex interpolation in a similar way as has been done in Chapter 5.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in R3, and Newton Polyhedra Detlef Müller

2014 ◽  
Keyword(s):  
Harmonic Analysis ◽  
Finite Type ◽  
Maximal Function ◽  
Oscillatory Integrals ◽  
The Other ◽  
Riemannian Surface ◽  
Fourier Restriction ◽  
Newton Polyhedra ◽  
The Given ◽  
Finite Type Hypersurfaces

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a smooth, finite type hypersurface in R³ with Riemannian surface measure dσ‎). The first problem is a classical question about estimates for oscillatory integrals, and there exists a huge body of results on it, in particular for convex hypersurfaces. The other two problems had first been formulated by Stein: the study of maximal averages along hypersurfaces has been initiated in Stein's work on the spherical maximal function, and also the idea of Fourier restriction goes back to him.

A Restriction Theorem for a k-Surface in ℝn

2005 ◽  
Vol 48 (2) ◽  
pp. 260-266 ◽  
Author(s):  
Daniel M. Oberlin
Keyword(s):  
Restriction Theorem ◽  
Fourier Restriction ◽  
Restriction Estimate

AbstractWe establish a sharp Fourier restriction estimate for a measure on a k-surface in ℝn, where n = k(k + 3)/2.

scholarly journals Some bounds for the degree of commutativity of a p-group of maximal class

1995 ◽  
Vol 51 (3) ◽  
pp. 353-367
Author(s):  
Antonio Vera-López ◽  
Gustavo A. Fernández-Alcober
Keyword(s):  
Maximal Subgroup ◽  
Lower Bounds ◽  
Nilpotency Class ◽  
The Other ◽  
Maximal Class ◽  
Derived Length ◽  
Other Hand

In this paper we obtain several lower bounds for the degree of commutativity of a p-group of maximal class of order pm. All the bounds known up to now involve the prime p and are almost useless for small m. We introduce a new invariant b which is related with the commutator structure of the group G and get a bound depending only on b and m, not on p. As a consequence, we bound the derived length of G and the nilpotency class of a certain maximal subgroup in terms of b. On the other hand, we also generalise some results of Blackburn. Examples are given in order to check the sharpness of the bounds.

ON BROADCASTING TIME

1999 ◽  
Vol 09 (01) ◽  
pp. 3-8
Author(s):  
VASSILIOS V. DIMAKOPOULOS ◽  
NIKITAS J. DIMOPOULOS
Keyword(s):  
Lower Bounds ◽  
Information Dissemination ◽  
Applied Mathematics ◽  
The Other ◽  
Arbitrary Graphs

Broadcasting is an information dissemination problem in which a particular node in a network must transmit an item of information to all the other nodes. In this work we present new lower bounds for the time needed to complete this process in arbitrary graphs. In particular we generalize a result of P. Fraigniaud and E. Lazard [Discrete Applied Mathematics, 53 (1994) 79–133] which states that if in a graph there are at least two vertices in distance equal to the diameter from the originator, then broadcasting requires time at least equal to the diameter plus one.

scholarly journals Testing methods for quantifying Monte Carlo variation for categorical variables in Probabilistic Genotyping

2021 ◽  
Author(s):  
Jo-Anne Bright ◽  
Duncan Alexander Taylor ◽  
James Michael Curran ◽  
JOHN BUCKLETON
Keyword(s):  
Monte Carlo ◽  
Lower Bound ◽  
Lower Bounds ◽  
Population Model ◽  
The Other ◽  
Categorical Variables ◽  
Testing Methods ◽  
Resampling Method

Two methods for applying a lower bound to the variation induced by the Monte Carlo effect are trialled. One of these is implemented in the widely used probabilistic genotyping system, STRmix Neither approach is giving the desired 99% coverage. In some cases the coverage is much lower than the desired 99%. The discrepancy (i.e. the distance between the LR corresponding to the desired coverage and the LR observed coverage at 99%) is not large. For example, the discrepancy of 0.23 for approach 1 suggests the lower bounds should be moved downwards by a factor of 1.7 to achieve the desired 99% coverage. Although less effective than desired these methods provide a layer of conservatism that is additional to the other layers. These other layers are from factors such as the conservatism within the sub-population model, the choice of conservative measures of co-ancestry, the consideration of relatives within the population and the resampling method used for allele probabilities, all of which tend to understate the strength of the findings.

scholarly journals Bounds for the Collapse Load of a Beam Compressed by Three Dies

1956 ◽  
Vol 9 (4) ◽  
pp. 419
Author(s):  
W Freiberger
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Lower Bounds ◽  
Limit Analysis ◽  
Velocity Fields ◽  
The Other ◽  
Upper And Lower Bounds ◽  
Collapse Load ◽  
Plastic Yielding ◽  
Plane Plastic

This paper deals with the problem of the plastic deformation of a beam under the action of three perfectly rough rigid dies, two dies applied to one side, one die to the other side of the beam, the single die being situated between the two others. It is treated as a problem of plane plastic flow. Discontinuous stress and velocity fields are assumed and upper and lower bounds for the pressure sufficient to cause pronounced plastic yielding determined by limit analysis.

TIME-OPTIMAL DIGITAL GEOMETRY ALGORITHMS ON MESHES WITH MULTIPLE BROADCASTING

1995 ◽  
Vol 09 (04) ◽  
pp. 601-613
Author(s):  
V. BOKKA ◽  
H. GURLA ◽  
S. OLARIU ◽  
J.L. SCHWING ◽  
I. STOJMENOVIĆ
Keyword(s):  
Lower Bound ◽  
Convex Hull ◽  
Lower Bounds ◽  
Minimum Distance ◽  
Fundamental Problem ◽  
Optimal Solution ◽  
The Other ◽  
Digital Geometry ◽  
Black Pixel ◽  
Time Optimal

The main contribution of this work is to show that a number of digital geometry problems can be solved elegantly on meshes with multiple broadcasting by using a time-optimal solution to the leftmost one problem as a basic subroutine. Consider a binary image pretiled onto a mesh with multiple broadcasting of size [Formula: see text] one pixel per processor. Our first contribution is to prove an Ω(n1/6) time lower bound for the problem of deciding whether the image contains at least one black pixel. We then obtain time lower bounds for many other digital geometry problems by reducing this fundamental problem to all the other problems of interest. Specifically, the problems that we address are: detecting whether an image contains at least one black pixel, computing the convex hull of the image, computing the diameter of an image, deciding whether a set of digital points is a digital line, computing the minimum distance between two images, deciding whether two images are linearly separable, computing the perimeter, area and width of a given image. Our second contribution is to show that the time lower bounds obtained are tight by exhibiting simple O(n1/6) time algorithms for these problems. As previously mentioned, an interesting feature of these algorithms is that they use, directly or indirectly, an algorithm for the leftmost one problem recently developed by one of the authors.

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