scholarly journals Enumeration of Lozenge Tilings of Halved Hexagons with a Boundary Defect

10.37236/5199 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Ranjan Rohatgi
Keyword(s):  
Factorization Theorem ◽  
Plane Partition ◽  
Weighted Version ◽  
Condensation Method ◽  
Boundary Defect ◽  
Lozenge Tilings ◽  
The Given ◽  
Special Case

We generalize a special case of a theorem of Proctor on the enumeration of lozenge tilings of a hexagon with a maximal staircase removed using Kuo’s graphical condensation method. Additionally, we prove a formula for a weighted version of the given region. The result also extends work of Ciucu and Fischer. By applying the factorization theorem of Ciucu, we are also able to generalize a special case of MacMahon’s boxed plane partition formula. 

scholarly journals A numerical technique for a general form of nonlinear fractional-order differential equations with the linear functional argument

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Khalid K. Ali ◽  
Mohamed A. Abd El salam ◽  
Emad M. H. Mohamed
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Order ◽  
Linear Functional ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Fractional Order Differential Equations ◽  
The Given ◽  
Functional Argument ◽  
Special Case

AbstractIn this paper, a numerical technique for a general form of nonlinear fractional-order differential equations with a linear functional argument using Chebyshev series is presented. The proposed equation with its linear functional argument represents a general form of delay and advanced nonlinear fractional-order differential equations. The spectral collocation method is extended to study this problem as a discretization scheme, where the fractional derivatives are defined in the Caputo sense. The collocation method transforms the given equation and conditions to algebraic nonlinear systems of equations with unknown Chebyshev coefficients. Additionally, we present a general form of the operational matrix for derivatives. A general form of the operational matrix to derivatives includes the fractional-order derivatives and the operational matrix of an ordinary derivative as a special case. To the best of our knowledge, there is no other work discussed this point. Numerical examples are given, and the obtained results show that the proposed method is very effective and convenient.

scholarly journals Positivity and Monotonicity Preserving Biquartic Rational Interpolation Spline Surface

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xinru Liu ◽  
Yuanpeng Zhu ◽  
Shengjun Liu
Keyword(s):  
Sufficient Conditions ◽  
Rational Interpolation ◽  
Rectangular Domain ◽  
Interpolation Spline ◽  
Spline Surface ◽  
Surface Data ◽  
Shape Preserving Interpolation ◽  
The Given ◽  
Surface Construction ◽  
Special Case

A biquartic rational interpolation spline surface over rectangular domain is constructed in this paper, which includes the classical bicubic Coons surface as a special case. Sufficient conditions for generating shape preserving interpolation splines for positive or monotonic surface data are deduced. The given numeric experiments show our method can deal with surface construction from positive or monotonic data effectively.

A Probability Scoring Rule for Simultaneous Events

2019 ◽  
Vol 16 (4) ◽  
pp. 301-313
Author(s):  
Andrew Grant ◽  
David Johnstone ◽  
Oh Kang Kwon
Keyword(s):  
Economic Benefit ◽  
Score Function ◽  
Interesting Property ◽  
Usual Sense ◽  
Power Utility ◽  
Scoring Rule ◽  
The Individual ◽  
Individual Scores ◽  
The Given ◽  
Special Case

We develop a scoring rule tailored to a decision maker who makes simultaneous bets on events that occur at times that require bets to be placed together. The rule proposed captures the economic benefit to a well-defined bettor who acts on one set of probabilities p against a baseline or rival set q. To allow for simultaneous bets, we assume a myopic power utility function with a risk aversion parameter tailored to suit the given user or application. Our score function is “proper” in the usual sense of motivating honesty. Apart from a special case of power utility, namely, log utility, the score is not “local,” which we excuse because a local scoring rule cannot capture the economic result that our score reflects. An interesting property of our rule is that the individual scores from individual events are multiplicative, rather than additive. Probability scores are often added to give a measure of aggregate performance over a set of trials. Our rule is unique in that scores must be multiplied to reach a meaningful aggregate.

scholarly journals COMPUTING SIGNED PERMUTATIONS OF POLYGONS

2011 ◽  
Vol 21 (01) ◽  
pp. 87-100
Author(s):  
GREG ALOUPIS ◽  
PROSENJIT BOSE ◽  
ERIK D. DEMAINE ◽  
STEFAN LANGERMAN ◽  
HENK MEIJER ◽  
...  
Keyword(s):  
Mirror Symmetry ◽  
Time Algorithm ◽  
Worst Case ◽  
Signed Permutations ◽  
Np Complete ◽  
Edge List ◽  
The Given ◽  
Special Case ◽  
Planar Polygon

Given a planar polygon (or chain) with a list of edges {e1, e2, e3, …, en-1, en}, we examine the effect of several operations that permute this edge list, resulting in the formation of a new polygon. The main operations that we consider are: reversals which involve inverting the order of a sublist, transpositions which involve interchanging subchains (sublists), and edge-swaps which are a special case and involve interchanging two consecutive edges. When each edge of the given polygon has also been assigned a direction we say that the polygon is signed. In this case any edge involved in a reversal changes direction. We show that a star-shaped polygon can be convexified using O(n2) edge-swaps, while maintaining simplicity, and that this is tight in the worst case. We show that determining whether a signed polygon P can be transformed to one that has rotational or mirror symmetry with P, using transpositions, takes Θ(n log n) time. We prove that the problem of deciding whether transpositions can modify a polygon to fit inside a rectangle is weakly NP-complete. Finally we give an O(n log n) time algorithm to compute the maximum endpoint distance for an oriented chain.

scholarly journals Plains in a Special Case. The Relationship Between the Planes

2021 ◽  
Vol 9 (11) ◽  
pp. 548-550
Author(s):  
Qozaqova Munojat Sharifjanovna
Keyword(s):  
Horizontal Projection ◽  
Straight Lines ◽  
The Given ◽  
The Relationship ◽  
Special Case

Annotation: To develop students' understanding of straight lines and planes and to develop skills and competencies in working on related issues. The listener must complete the given task on A4 paper with the necessary tools. Keywords: straight lines, perpendicular, horizontal projection, frontal projections.

Model‐driven predictive deconvolution

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 713-722 ◽  
Author(s):  
Enders A. Robinson
Keyword(s):  
Prediction Error ◽  
Leading Edge ◽  
Arbitrary Length ◽  
Model Driven ◽  
Phase Rotation ◽  
Predictive Deconvolution ◽  
Minimum Delay ◽  
The Given ◽  
Special Case

A gap‐deconvolution filter with gap α is defined as the prediction error operator with prediction distance α. A spike‐deconvolution filter is defined as the prediction error operator with prediction distance unity. That is, a spike‐deconvolution filter is the special case of a gap‐deconvolution filter with gap equal to one time unit. Generally, the designation “gap deconvolution” is reserved for the case when α is greater than one, and the term “spike deconvolution” is used when α is equal to one. It is often stated that gap deconvolution with gap α shortens an input wavelet of arbitrary length to an output wavelet of length α (or less). Since an arbitrary value of α can be chosen, it would follow that resolution or wavelet contraction may be controlled by use of gap deconvolution. In general, this characterization of gap deconvolution is true for arbitrary α if and only if the wavelet is minimum delay (i.e., minimum phase). The method of model‐driven deconvolution can be used in the case of a nonminimum‐delay wavelet. The wavelet is the convolution of a minimum‐delay reverberation and a short nonminimum‐delay orphan. The model specifies that the given trace is the convolution of the white reflectivity and this nonminimum‐delay wavelet. The given trace yields the spike‐deconvolution filter and its inverse. These two signals are then used to compute the gap‐deconvolution filters and their inverses for various prediction distances. The inverses are examined, and a stable one is picked as the most likely minimum‐delay reverberation. The corresponding gap‐deconvolution filter is the optimum one for the removal of this minimum‐delay reverberation from the given trace. As a byproduct, the minimum‐delay counterpart of the orphan can be obtained. The optimum gap‐deconvolved trace is examined for zones that contain little activity, and the leading edge of the wavelet following such a zone is chosen. Next, the phase of the minimum‐delay counterpart of the orphan is rotated until it fits the extracted leading edge. From the amount of phase rotation, the required phase‐correcting filter can be estimated. Alternatively, downhole information, if available, can be used to estimate the phase‐correcting filter. Application of the phase‐correcting filter to the spike‐deconvolved trace gives the required approximation to the reflectivity. As a final step, wavelet processing can be applied to yield a final interpreter trace made up of zero‐phase wavelets.

Spinwellen in dünnen ferromagnetischen Schichten

1964 ◽  
Vol 19 (13) ◽  
pp. 1567-1580 ◽  
Author(s):  
Rainer Jelitto
Keyword(s):  
Difference Equation ◽  
Surface States ◽  
Subsequent Paper ◽  
Cubic Lattice ◽  
Starting Point ◽  
Transcendental Equations ◽  
The One ◽  
The Given ◽  
Special Case ◽  
General Method

This paper is concerned with an ideal spin-l/2-HEisENBERG-model for thin ferromagnetic films. A general method is given for the calculation of the one-spinwave eigenstates and their spectrum in dependence on the lattice type and the orientation of the surfaces of the film. The function that characterises the shape of the spinwave perpendicular to the film must fulfil a linear eigenvalue-difference-equation as well as a set of boundary conditions.For next-neighbour interactions this system may be evaluated for an especially simple case. For it spinwavestates of the form of cos-sin-functions as well as surface states are found. Their momenta are given by some transcendental equations, which are discussed.For all other cases the given difference-equation cannot be solved in a closed form, but at any rate it is a starting point for numerical calculations.In a subsequent paper it will be shown that the special case mentioned above covers some important surface orientations of the cubic lattice types. For films of these orientations the dependence of the magnetization on temperature and thickness of the film will be derived from the spinwave spectra.

An interesting fact regarding the Routh table

2009 ◽  
Vol 223 (5) ◽  
pp. 709-711
Author(s):  
R Landers
Keyword(s):  
Technical Note ◽  
Analysis Tool ◽  
Positive Real ◽  
Interesting Fact ◽  
The Given ◽  
Special Case

The Routh table is a powerful analysis tool used to determine how many roots of a given polynomial have negative, zero, and positive real parts. A special case occurs when a row of zeros is encountered. This indicates an even polynomial may be factored from the given polynomial. It is well known that the even polynomial is in the row above the row of zeros. In this technical note it will be shown that the even polynomial may be factored from all of the polynomials in the rows above the row of zeros.

scholarly journals Base change for ramified unitary groups: The strongly ramified case

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Corinne Blondel ◽  
Geo Kam-Fai Tam
Keyword(s):  
Unitary Group ◽  
Base Change ◽  
Supercuspidal Representation ◽  
Supercuspidal Representations ◽  
Parabolic Induction ◽  
Level Zero ◽  
Simple Character ◽  
The Given ◽  
Special Case ◽  
Residual Characteristic

Abstract We compute a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. In this special case, we require the given supercuspidal representation to contain a skew maximal simple stratum, and the field datum of this stratum to be of maximal degree, tamely ramified over the base field, and quadratic ramified over its subfield fixed by the Galois involution that defines the unitary group. The base change of this supercuspidal representation is described by a canonical lifting of its underlying simple character, together with the base change of the level-zero component of its inducing cuspidal type, modified by a sign attached to a quadratic Gauss sum defined by the internal structure of the simple character. To obtain this result, we study the reducibility points of a parabolic induction and the corresponding module over the affine Hecke algebra, defined by the covering type over the product of types of the given supercuspidal representation and of a candidate of its base change.

scholarly journals Heuristic approach to train rescheduling

2007 ◽  
Vol 17 (1) ◽  
pp. 9-29 ◽  
Author(s):  
Snezana Mladenovic ◽  
Mirjana Cangalovic
Keyword(s):  
Objective Function ◽  
Job Shop ◽  
Heuristic Algorithms ◽  
Job Shop Scheduling ◽  
Programming Approach ◽  
Job Shop Scheduling Problem ◽  
Time Performance ◽  
Train Rescheduling ◽  
The Given ◽  
Special Case

Starting from the defined network topology and the timetable assigned beforehand, the paper considers a train rescheduling in respond to disturbances that have occurred. Assuming that the train trips are jobs, which require the elements of infrastructure - resources, it was done by the mapping of the initial problem into a special case of job shop scheduling problem. In order to solve the given problem, a constraint programming approach has been used. A support to fast finding "enough good" schedules is offered by original separation, bound and search heuristic algorithms. In addition, to improve the time performance, instead of the actual objective function with a large domain, a surrogate objective function is used with a smaller domain, if there is such. .

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