scholarly journals Isospectral hermitian counterpart of complex nonhermitian Hamiltonian p2 – gx4 + a/x2

2013 ◽  
Vol 91 (8) ◽  
pp. 599-603 ◽  
Author(s):  
Asiri Nanayakkara ◽  
Thilagarajah Mathanaranjan
Keyword(s):  
New Class ◽  
Special Case ◽  
Hamiltonian Pair

We show that the nonhermitian Hamiltonians H = p2 – gx4 + a/x2 and the conventional hermitian Hamiltonians h = p2 + 4gx4 + bx [Formula: see text] are isospectral if a = (b2 – 4gℏ2)/16g and a ≥ –ℏ2/4. This new class includes the equivalent nonhermitian–hermitian Hamiltonian pair, p2 – gx4 and [Formula: see text] found by Jones and Mateo six years ago as a special case. When a = (b2 – 4gℏ2)/16g and a < –ℏ2/4 although h and H are still isospectral, b is pure imaginary, and h is no longer the hermitian counterpart of H.

scholarly journals On the ergodic distribution of oscillating queueing systems

2003 ◽  
Vol 16 (4) ◽  
pp. 311-326 ◽  
Author(s):  
Mykola Bratiychuk ◽  
Andrzej Chydzinski
Keyword(s):  
Queueing Systems ◽  
Numerical Example ◽  
New Class ◽  
Ergodic Distribution ◽  
Number Of Customers ◽  
Special Case

This paper examines a new class of queueing systems and proves a theorem on the existence of the ergodic distribution of the number of customers in such a system. An ergodic distribution is computed explicitly for the special case of a G/M−M/1 system, where the interarrival distribution does not change and both service distributions are exponential. A numerical example is also given.

scholarly journals The Inverse Lomax-G Family with application to Breaking Strength Data

2020 ◽  
pp. 49-60
Author(s):  
Jamilu Yunusa Falgore ◽  
Sani Ibrahim Doguwa
Keyword(s):  
Breaking Strength ◽  
Moment Generating Function ◽  
Maximum Likelihood Estimates ◽  
Strength Data ◽  
New Class ◽  
Class A ◽  
New Family ◽  
Competing Models ◽  
Special Case ◽  
Study Application

We proposed a new class of distributions with two additional positive parameters called the Inverse Lomax-G (IL-G) class. A special case was discussed, by taking Weibull as a baseline. Different properties of the new family that hold for any type of baseline model are derived including moments, moment generating function, entropy for Renyi, entropy for Shanon, and order statistics. The performances of the maximum likelihood estimates of the parameters of the sub-model of the Inverse Lomax-G family were evaluated through a simulation study. Application of the sub-model to the Breaking strength data clearly showed its superiority overthe other competing models.

scholarly journals Global Analysis and the Periodic Character of a Class of Difference Equations

Axioms ◽  
2019 ◽  
Vol 8 (4) ◽  
pp. 131 ◽  
Author(s):  
George E. Chatzarakis ◽  
Elmetwally M. Elabbasy ◽  
Osama Moaaz ◽  
Hamida Mahjoub
Keyword(s):  
Mathematical Models ◽  
Difference Equations ◽  
Global Analysis ◽  
New Class ◽  
Special Case ◽  
Life Phenomenon

In biology, Difference equations is often used to understand and describe life phenomenon through mathematical models. So, In this work, we study a new class of difference equations by focusing on the periodicity character, stability (local and global) and boundedness of its solutions. Furthermore, this equation involves a May’s Host Parasitoid Model, as a special case.

scholarly journals A Parametric Generalization of the Baskakov-Schurer-Szász-Stancu Approximation Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 980
Author(s):  
Naim Latif Braha ◽  
Toufik Mansour ◽  
Hari Mohan Srivastava
Keyword(s):  
Type Theorem ◽  
Weighted Spaces ◽  
Shape Preserving ◽  
Korovkin Type Theorem ◽  
Stancu Operators ◽  
New Class ◽  
Approximation Operators ◽  
Voronovskaya Type Theorem ◽  
Shape Preserving Properties ◽  
Special Case

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators.

scholarly journals On the link pattern distribution of quarter-turn symmetric FPL configurations

2008 ◽  
Vol DMTCS Proceedings vol. AJ,... (Proceedings) ◽  
Author(s):  
Philippe Duchon
Keyword(s):  
Nous Obtenons ◽  
Plane Partitions ◽  
New Class ◽  
International Audience ◽  
Pattern Distribution ◽  
Special Case ◽  
Link Pattern

International audience We present new conjectures on the distribution of link patterns for fully-packed loop (FPL) configurations that are invariant, or almost invariant, under a quarter turn rotation, extending previous conjectures of Razumov and Stroganov and of de Gier. We prove a special case, showing that the link pattern that is conjectured to be the rarest does have the prescribed probability. As a byproduct, we get a formula for the enumeration of a new class of quasi-symmetry of plane partitions. Nous présentons de nouvelles conjectures portant sur la distribution des schémas de couplage des configurations de boucles compactes (FPL) invariantes, ou presque invariantes, par une rotation d'un quart de tour. Ces nouvelles conjectures étendent des conjectures précédentes dues à Razumov et Stroganov et à de Gier. Dans chaque cas, nous prouvons un cas particulier, en démontrant que le schéma de couplage conjecturé pour être le plus rare a effectivement la probabilité prédite. Nous obtenons également une formule pour l'énumération d'une nouvelle classe de quasi-symétrie de partitions planes.

A generalization of Trenkler’s magic cubes formula

2017 ◽  
Vol 4 (8) ◽  
pp. 39-45
Author(s):  
Livinus U. Uko ◽  
Terry L. Barron
Keyword(s):  
General Class ◽  
Sufficient Conditions ◽  
New Class ◽  
Odd Order ◽  
Magic Cube ◽  
Special Case

Abstract A Magic Cube of order p is a p×p×p cubical array with non-repeated entries from the set {1, 2, . . . , p3} such that all rows, columns, pillars and space diagonals have the same sum. In this paper, we show that a formula introduced in The Mathematical Gazette 84(2000), by M. Trenkler, for generating odd order magic cubes is a special case of a more general class of formulas. We derive sufficient conditions for the formulas in the new class to generate magic cubes, and we refer to the resulting class as regular magic cubes. We illustrate these ideas by deriving three new formulas that generate magic cubes of odd order that differ from each other and from the magic cubes generated with Trenkler’s rule.

scholarly journals A Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEs

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
I. B. Aiguobasimwin ◽  
R. I. Okuonghae
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Initial Value Problems ◽  
Initial Value ◽  
Large Interval ◽  
New Class ◽  
Second Derivatives ◽  
Stiff Odes ◽  
Runge Kutta ◽  
Special Case

In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered. The TDTSRK methods are a special case of multi-derivative Runge-Kutta methods proposed by Kastlunger and Wanner (1972). The methods considered herein incorporate only the first and second derivatives terms of ODEs. These methods possess large interval of stability when compared with other existing methods in the literature. The experiments have been performed on standard problems, and comparisons were made with some standard explicit Runge-Kutta methods in the literature.

scholarly journals The The Topp Leone-G Power Series Class of Distributions with Applications

2021 ◽  
pp. 827-846
Author(s):  
Fastel Chipepa ◽  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Kethamile Rannona
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Poisson Distribution ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
Proposed Model ◽  
Special Case

We present a new class of distributions called the Topp-Leone-G Power Series (TL-GPS) class of distributions. This model is obtained by compounding the Topp-Leone-G distribution with the power series distribution. Statistical prop- erties of the TL-GPS class of distributions are obtained. Maximum likelihood estimates for the proposed model were obtained. A simulation study is carried out for the special case of Topp-Leone Log-Logistic Poisson distribution to assess the performance of the maximum likelihood estimates. Finally, we apply Topp-Leone-log-logistic Poisson distribution to real data sets to illustrate the usefulness and applicability of the proposed class of distributions.

scholarly journals Construction of the Type 2 Degenerate Multi-Poly-Euler Polynomials and Numbers

2020 ◽  
Author(s):  
Waseem Ahmad Khan ◽  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Linear Combination ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
Addition Formula ◽  
New Class ◽  
Whitney Numbers ◽  
Derivative Formula ◽  
Euler Polynomials And Numbers ◽  
Special Case

In this paper, we consider a new class of polynomials which is called the multi-poly-Euler polynomials. Then, we investigate their some properties and relations. We provide that the type 2 degenerate multi-poly-Euler polynomials equals a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind. Moreover, we provide an addition formula and a derivative formula. Furthermore, in a special case, we acquire a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers.

scholarly journals On Multiply Robust Mendelian Randomization (MR2) With Many Invalid Genetic Instruments

2021 ◽  
Author(s):  
Baoluo Sun ◽  
Zhonghua Liu ◽  
Eric Tchetgen Tchetgen
Keyword(s):  
Large Scale ◽  
Mendelian Randomization ◽  
Causal Effect ◽  
New Class ◽  
Large Scale Analysis ◽  
Empirical Performance ◽  
Class Of Estimators ◽  
Semiparametric Theory ◽  
Semiparametric Efficiency Bound ◽  
Special Case

Mendelian randomization (MR) is a popular instrumental variable (IV) approach, in which genetic markers are used as IVs. In order to improve efficiency, multiple markers are routinely used in MR analyses, leading to concerns about bias due to possible violation of IV exclusion restriction of no direct effect of any IV on the outcome other than through the exposure in view. To address this concern, we introduce a new class of Multiply Robust MR (MR2) estimators that are guaranteed to remain consistent for the causal effect of interest provided that at least one genetic marker is a valid IV without necessarily knowing which IVs are invalid. We show that the proposed MR2 estimators are a special case of a more general class of estimators that remain consistent provided that a set of at least k† out of K candidate instrumental variables are valid, for k† ≤ K set by the analyst ex ante, without necessarily knowing which IVs are invalid. We provide formal semiparametric theory supporting our results, and characterize the semiparametric efficiency bound for the exposure causal effect which cannot be improved upon by any regular estimator with our favorable robustness property. We conduct extensive simulation studies and apply our methods to a large-scale analysis of UK Biobank data, demonstrating the superior empirical performance of MR2 compared to competing MR methods.

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