scholarly journals Identities involving 3-variable Hermite polynomials arising from umbral method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Nusrat Raza ◽  
Umme Zainab ◽  
Serkan Araci ◽  
Ayhan Esi
Keyword(s):  
Hermite Polynomials ◽  
Special Cases

AbstractIn this paper, we employ an umbral method to reformulate the 3-variable Hermite polynomials and introduce the 4-parameter 3-variable Hermite polynomials. We also obtain some new properties for these polynomials. Moreover, some special cases are discussed and some concluding remarks are also given.

Random Vibrations in Discrete Nonlinear Dynamic Systems

1968 ◽  
Vol 10 (2) ◽  
pp. 168-174 ◽  
Author(s):  
R. G. Bhandari ◽  
R. E. Sherrer
Keyword(s):  
Exact Solutions ◽  
Density Function ◽  
Gaussian White Noise ◽  
Hermite Polynomials ◽  
Planck Equation ◽  
Degree Of Freedom ◽  
Multiple Series ◽  
Special Cases ◽  
Fokker Planck Equations ◽  
Fokker Planck

A one-degree-of-freedom system and a two-degree-of-freedom system containing Dis-placement and velocity dependent nonlinearities subjected to stationary gaussian white noise excitation have been studied by the method of the Fokker-Planck equation. Non-linearities have been represented by suitable polynomials. The Fokker-Planck equations governing the stationary probability density function for these systems have been solved by representing the density function by a multiple series of Hermite polynomials. The constants in the series expansion were determined by Galerkin's method. Analysis is developed for the system containing nonlinearities described by suitable polynomials in velocity and displacement dependent forces. Comparisons were made between series and exact solutions for those special cases for which exact solutions are known.

STEERABILITY OF HERMITE KERNEL

2013 ◽  
Vol 27 (04) ◽  
pp. 1354006 ◽  
Author(s):  
BO YANG ◽  
JAN FLUSSER ◽  
TOMÁŠ SUK
Keyword(s):  
Image Processing ◽  
Computer Vision ◽  
High Efficiency ◽  
Hermite Polynomials ◽  
Gaussian Function ◽  
Kernel Functions ◽  
Hermite Functions ◽  
Interpolation Function ◽  
Special Cases ◽  
Potential Applications

Steerability is a useful and important property of "kernel" functions. It enables certain complicated operations involving orientation manipulation on images to be executed with high efficiency. Thus, we focus our attention on the steerability of Hermite polynomials and their versions modulated by the Gaussian function with different powers, defined as the Hermite kernel. Certain special cases of such kernel, Hermite polynomials, Hermite functions and Gaussian derivatives are discussed in detail. Correspondingly, these cases demonstrate that the Hermite kernel is a powerful and effective tool for image processing. Furthermore, the steerability of the Hermite kernel is proved with the help of a property of Hermite polynomials revealing the rule concerning the product of two Hermite polynomials after coordination rotation. Consequently, any order of the Hermite kernel inherits steerability. Moreover, a couple sets of an explicit interpolation function and basis function can be directly obtained. We provide some examples to verify steerability of the Hermite kernel. Experimental results show the effectiveness of steerability and its potential applications in the fields of image processing and computer vision.

scholarly journals Generalized q-Laguerre type polynomials and q-partial differential equations

Filomat ◽  
2019 ◽  
Vol 33 (5) ◽  
pp. 1403-1415
Author(s):  
Da-Wei Niu
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Generating Functions ◽  
Final Section ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Partial Differential ◽  
Integral Formulas ◽  
Special Cases

In this paper we define the q-Laguerre type polynomials Un(x; y; z; q), which include q-Laguerre polynomials, generalized Stieltjes-Wigert polynomials, little q-Laguerre polynomials and q-Hermite polynomials as special cases. We also establish a generalized q-differential operator, with which we build the relations between analytic functions and Un(x; y; z; q) by using certain q-partial differential equations. Therefore, the corresponding conclusions about q-Laguerre polynomials, little q-Laguerre polynomials and q-Hermite polynomials are gained as corollaries. As applications, some generating functions and generalized Andrews-Askey integral formulas are given in the final section.

scholarly journals Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach

2019 ◽  
Vol 10 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Clemente Cesarano
Keyword(s):  
Chebyshev Polynomials ◽  
Polynomial Interpolation ◽  
Hermite Polynomials ◽  
Integral Transforms ◽  
Multi Index ◽  
Special Cases ◽  
The Laplace Transform ◽  
Translation Operators ◽  
Sturm Liouville ◽  
Symbolic Approach

Abstract Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

Decoration technique and surface physics

1978 ◽  
Vol 36 (1) ◽  
pp. 436-437 ◽  
Author(s):  
H. Bethge
Keyword(s):  
Diffusion Path ◽  
Special Importance ◽  
Surface Physics ◽  
Step Structure ◽  
Initial Stage ◽  
Special Cases ◽  
Atomic Surface ◽  
The Mean ◽  
Bulk Structure ◽  
Decoration Technique

Besides the atomic surface structure, diverging in special cases with respect to the bulk structure, the real structure of a surface Is determined by the step structure. Using the decoration technique /1/ it is possible to image step structures having step heights down to a single lattice plane distance electron-microscopically. For a number of problems the knowledge of the monatomic step structures is important, because numerous problems of surface physics are directly connected with processes taking place at these steps, e.g. crystal growth or evaporation, sorption and nucleatlon as initial stage of overgrowth of thin films.To demonstrate the decoration technique by means of evaporation of heavy metals Fig. 1 from our former investigations shows the monatomic step structure of an evaporated NaCI crystal. of special Importance Is the detection of the movement of steps during the growth or evaporation of a crystal. From the velocity of a step fundamental quantities for the molecular processes can be determined, e.g. the mean free diffusion path of molecules.

One Size Fits All?

Methodology ◽  
2012 ◽  
Vol 8 (1) ◽  
pp. 23-38 ◽  
Author(s):  
Manuel C. Voelkle ◽  
Patrick E. McKnight
Keyword(s):  
Repeated Measures ◽  
Structural Equation ◽  
Type I Error ◽  
Equation Modeling ◽  
Type I ◽  
Finite Sample ◽  
Traditional Methods ◽  
Repeated Measures Anova ◽  
Special Cases ◽  
Latent Curve

The use of latent curve models (LCMs) has increased almost exponentially during the last decade. Oftentimes, researchers regard LCM as a “new” method to analyze change with little attention paid to the fact that the technique was originally introduced as an “alternative to standard repeated measures ANOVA and first-order auto-regressive methods” (Meredith & Tisak, 1990, p. 107). In the first part of the paper, this close relationship is reviewed, and it is demonstrated how “traditional” methods, such as the repeated measures ANOVA, and MANOVA, can be formulated as LCMs. Given that latent curve modeling is essentially a large-sample technique, compared to “traditional” finite-sample approaches, the second part of the paper addresses the question to what degree the more flexible LCMs can actually replace some of the older tests by means of a Monte-Carlo simulation. In addition, a structural equation modeling alternative to Mauchly’s (1940) test of sphericity is explored. Although “traditional” methods may be expressed as special cases of more general LCMs, we found the equivalence holds only asymptotically. For practical purposes, however, no approach always outperformed the other alternatives in terms of power and type I error, so the best method to be used depends on the situation. We provide detailed recommendations of when to use which method.

Penile Fracture-Report of Two Cases and Review of Current Literature

KYAMC Journal ◽  
2019 ◽  
Vol 10 (2) ◽  
pp. 122-125
Author(s):  
Ashraf Uddin Mallik ◽  
Mostafizur Rahman ◽  
Fatema Bagum ◽  
Uttam Karmaker ◽  
Baikali Ferdous ◽  
...  
Keyword(s):  
Tunica Albuginea ◽  
Traumatic Rupture ◽  
Penile Fracture ◽  
Corpora Cavernosa ◽  
Effective Treatment Modality ◽  
Special Cases ◽  
History Of ◽  
Penile Injury ◽  
Urological Emergency ◽  
Erect Penis

Penile fracture is an uncommon urological emergency, especially in Bangladesh. The other name is traumatic rupture of the tunica albuginea and corpora cavernosa in the erect penis. It occurs when an erect penis face to buckle under the pressure of a blunt sexual trauma. Patient gives the typical history of immediate detumescence, severe pain, swelling and eggplant deformity of the penile shaft due to penile injury. Immediate surgical exploration and repair of corpora Cavernosa with tunica albugenia is the most effective treatment modality. In normal cases diagnosis is made from history, physical examination alone. In some special cases ultrasonogram, radiological images, including retrograde urethrography or cavernosography are mandatory for proper diagnosis. KYAMC Journal Vol. 10, No.-2, July 2019, Page 122-125

Computing Cores for Existential Rules with the Standard Chase and ASP

2020 ◽  
Author(s):  
Markus Krötzsch
Keyword(s):  
Large Class ◽  
Data Exchange ◽  
Answer Set Programming ◽  
Query Answering ◽  
Universal Model ◽  
The Core ◽  
Universal Models ◽  
General Terms ◽  
Special Cases ◽  
The Many

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

CURRENT SITUATION OF MANAGEMENT AND USE OF TEACHING EQUIPMENT UNDER ORIENTATIONS FOR DEVELOPING STUDENT CAPACITY IN LOWER SECONDARY SCHOOLS IN DIEN BIEN DISTRICT, DIEN BIEN PROVINCE IN THE PRESENT PERIOD

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Pham Van Phuc ◽  
Ngo Quang Son
Keyword(s):  
Secondary Schools ◽  
Teaching Methods ◽  
Time Management ◽  
Current Trend ◽  
Equipment Management ◽  
Full Time ◽  
Special Cases ◽  
Effective Use ◽  
Lower Secondary Schools

Last time, management of equipment, maintenance and use of teaching equipment in lower secondary schools in Dien Bien district, Dien Bien province has been paid more attention, making important contributions to keeping sustainably, improve the quality of education in the district. Every year the lower secondary schools have been given funding and have plans to equip additional teaching equipment. Most lower secondary schools have full-time staff in charge of teaching equipment; with equipment storage rooms, cabinets are gradually added; laboratories and classrooms have been built more and more; have a system of records of teaching equipment management established; The work of inventorying and purifying teaching equipment periodically was also concerned. The movement of innovating teaching methods has made education managers and teachers more interested in using teaching equipment effectively. The positive management measures have caused many teachers to use teaching equipment as an integral part of the lesson, helping the quality of the lessons be increasingly improved to meet the requirements of changes. New teaching methods. Education administrators, teachers, teaching equipment staff are becoming more and more serious in teaching device management. However, the reality of teaching equipment management still reveals many limitations: The management of teaching equipment in schools is still administrative and ineffective. The equipment has no overall and detailed plans; The procurement of teaching equipment is not guaranteed in terms of quantity, lack of uniformity (some are redundant, some are lacking), quality is limited (durability, accuracy is not guaranteed, some new ones are not used); preservation still has many shortcomings; lack of specialized staff; lack of storage space or insufficient storage; lack of cabinets, prices, laboratories, subject classrooms; specially managing the use of teaching equipment is not tight; Many places teachers have not paid attention to use, ineffective use. The situation of “teaching vegetarianism” is still common, teaching equipment used is still movement, mostly used only in special cases such as competitions for good teachers, lectures or when there is a delegation check; There are many cases of information technology abuse in teaching. The effective use of teaching equipment oriented student capacity development is not much. The management of the use of teaching equipment oriented to develop student competencies in the current trend of Industry Revolution 4.0 is a matter of great concern to educational managers.Thus, the task of surveying the situation of managing the effective use of teaching equipment, finding subjective and objective reasons in order to propose measures to effectively manage the use of teaching equipment in the direction of developing students’ practical capacities and contributing to improving the quality of teaching in secondary schools in Dien Bien district, Dien Bien province is a very important and necessary task today.

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