scholarly journals Case Study: Coefficient Training in Paley-Wiener Space, FFT, and Wavelet Theory

2021 ◽  
Author(s):  
Kayupe Kikodio Patrick
Keyword(s):  
Coherent State ◽  
Bessel Functions ◽  
Special Functions ◽  
Wiener Space ◽  
State Transformation ◽  
Wavelet Theory ◽  
Almost Everywhere ◽  
Special Case ◽  
Cylindrical Harmonics

Bessel functions form an important class of special functions and are applied almost everywhere in mathematical physics. They are also called cylindrical functions, or cylindrical harmonics. This chapter is devoted to the construction of the generalized coherent state (GCS) and the theory of Bessel wavelets. The GCS is built by replacing the coefficient zn/n!,z∈C of the canonical CS by the cylindrical Bessel functions. Then, the Paley-Wiener space PW1 is discussed in the framework of a set of GCS related to the cylindrical Bessel functions and to the Legendre oscillator. We prove that the kernel of the finite Fourier transform (FFT) of L2-functions supported on −11 form a set of GCS. Otherwise, the wavelet transform is the special case of CS associated respectively with the Weyl-Heisenberg group (which gives the canonical CS) and with the affine group on the line. We recall the wavelet theory on R. As an application, we discuss the continuous Bessel wavelet. Thus, coherent state transformation (CST) and continuous Bessel wavelet transformation (CBWT) are defined. This chapter is mainly devoted to the application of the Bessel function.

JAYNES-CUMMINGS MODEL AS A CASE STUDY FOR THE DERIVATION OF TIME-DEPENDENT SCHRÖDINGER EQUATION

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4557-4564
Author(s):  
SUPITCH KHEMMANI ◽  
VIRULH SA-YAKANIT
Keyword(s):  
Schrödinger Equation ◽  
Coherent State ◽  
Linear Combination ◽  
Schrodinger Equation ◽  
Time Dependent ◽  
State Representation ◽  
Field System ◽  
Single State ◽  
Special Case

The derivation of a time-dependent Schrödinger equation (TDSE) from a time-independent Schrödinger equation (TISE) in the coherent state representation is considered for the special case of a simple coupled atom-field system described by the soluble Jaynes-Cummings model. The derivation shows why, from the outset, a linear combination of energy eigenstates, instead of a single state, must be used in order to obtain a TDSE for general states. Moreover, this study leads to a method of solving a TDSE by simply solving a TISE.

Nonwovens: Global Trends in World Economy, European Foreign Trade, and Selected Case Studies from Poland and Asian Brics Countries

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zofia Wysokińska ◽  
Tomasz Czajkowski ◽  
Katarzyna Grabowska
Keyword(s):  
Case Studies ◽  
World Economy ◽  
World Market ◽  
Global Trends ◽  
Textile Materials ◽  
Brics Countries ◽  
Recent Trends ◽  
Almost All ◽  
Special Case

AbstractNonwovens are one of the most versatile textile materials and have become increasingly popular in almost all sectors of the economy due to their low manufacturing costs and unique properties. In the next few years, the world market of nonwovens is predicted to grow by 7%–8% annually (International Nonwovens & Disposables Association [INDA], European Disposables and Nonwovens Association [EDANA], and Markets and Markets). This article aims to analyze the most recent trends in the global export and import of nonwovens, to present two case studies of Polish companies that produce them, and to present one special case study of the market of nonwoven geotextiles in China and India, which are the Asian transition economies among the BRICS countries (Brazil, Russia, India, China, and South Africa).

Management of Optic Neuritis in Ayurveda - A Special Case Report

2018 ◽  
Vol 3 (5) ◽  
Author(s):  
Dr. Harsha S. ◽  
Dr. Mamatha KV.
Keyword(s):  
Optic Nerve ◽  
Optic Neuritis ◽  
Visual Information ◽  
Vision Loss ◽  
Specific Treatment ◽  
Interesting Case ◽  
Treatment Modalities ◽  
Further Development ◽  
Special Case

The optic nerve carries visual information from your eye to your brain. Optic neuritis is when your optic nerve becomes inflamed. Optic neuritis can flare up suddenly from an infection or nerve disease. The inflammation usually causes temporary vision loss that typically happens in only one eye. Those with Optic neuritis sometimes experience pain. As you recover and the inflammation goes away, your vision will likely return. There are no direct references in our classics regarding optic neuritis but can be contemplated as a condition by name Parimlayi Timira. The specific management as such is not cited but a transcendence approach can be done with adopting the treatment which has the ability to pacify the already occurred pathology and prevent the further development of the disease. One such interesting case study on Optic neuritis is elaborated here where in specific treatment modalities (Shodana, Shamana and Kriyakalpas) played role in pacifying the condition.

scholarly journals Construction of All-Wood Trusses with Plywood Nodes and Wooden Pegs: A Strategy towards Resource-Efficient Timber Construction

2021 ◽  
Vol 11 (6) ◽  
pp. 2568
Author(s):  
Benjamin Kromoser ◽  
Matthias Braun ◽  
Maximilian Ortner
Keyword(s):  
Environmental Impact ◽  
Parametric Design ◽  
Gusset Plates ◽  
Research Areas ◽  
Timber Construction ◽  
First Results ◽  
Building Components ◽  
Numerical Optimisation ◽  
Special Case

Timber truss systems are very efficient load-bearing structures. They allow for great freedom in design and are characterised by high material use in combination with a low environmental impact. Unfortunately, the extensive effort in design and production have made the manufacturing and application of these structures, in this day and age, a rarity. In addition, the currently mainly used steel gusset plates adversely affect the costs and environmental impact of the trusses. The authors’ goals are to optimise the design of timber trusses and to solely use wood for all building components. The two research areas, (1) optimisation of the truss geometry and (2) optimisation of the joints by using solely wood–wood connections, are addressed in this paper. The numerical optimisation strategy is based on a parametric design of the truss and the use of a genetic solver for the optimisation regarding minimal material consumption. Furthermore, first results of the tensile and compression behaviour of the chosen wood–wood connections are presented. The basic idea for the joints is to use a plywood plate as a connector, which is inserted into the truss members and fixed with wooden pegs. The housing of the new robot laboratory located at BOKU Vienna is considered a special case study for the research and serves as an accompanying example for the application of the research within the present paper.

scholarly journals Irreversibility process characteristics of variant viscosity and conductivity on hybrid nanofluid flow through Poiseuille microchannel: A special case study

2021 ◽  
pp. 101337
Author(s):  
Suriya Uma Devi. S ◽  
Fazle Mabood ◽  
Wasim Jamshed ◽  
S.R. Mishra ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Process Characteristics ◽  
Flow Through ◽  
Special Case

scholarly journals Diaphyseal pseudarthrosis of the femur in a patient with poliomyelitis. A special case study

2018 ◽  
Vol 81 ◽  
pp. 51-54
Author(s):  
J.A. Enríquez-Castro ◽  
G. Estévez-Díaz ◽  
A.F. Sánchez-Chávez ◽  
S.I. García-García ◽  
A. Saldaña-García
Keyword(s):  
Special Case

The Unified Theory of Tubesheet Design - Part III: Comparison with ASME Method and Case Study

2021 ◽  
Author(s):  
Hong-Song Zhu ◽  
Jinguo Zhai ◽  
Guo-Yan Zhou
Keyword(s):  
Heat Exchangers ◽  
Numerical Comparison ◽  
Unified Theory ◽  
Element Analysis ◽  
Theoretical Comparison ◽  
Comparison Results ◽  
Different Types ◽  
Special Case ◽  
Simplified Mechanical Model

Abstract Based on the unified theory of tubesheet (TS) design for fixed TS heat exchangers (HEX), floating head and U-tube HEX presented in Part I and Part II, theoretical and numerical comparisons with ASME method are performed in this paper as Part III. Theoretical comparison shows that ASME method can be obtained from the special case of the simplified mechanical model of the unified theory. Numerical Comparison results indicate that predictions given by the unified theory agree well with finite element analysis (FEA), while ASME results are not accurate or not correct. Therefore, it is concluded that the unified theory deals with different types of HEX in equal detail with confidence to predict design stresses.

scholarly journals Heuristics Algorithms for a Heterogeneous Fleets VRP with Excessive Demand for the Vehicle at the Pickup Points, and the Longest Traveling Time Constraint: A Case Study in Prasitsuksa Songkloe, Ubonratchathani Thailand

Logistics ◽  
2018 ◽  
Vol 2 (3) ◽  
pp. 15 ◽  
Author(s):  
Sasitorn Kaewman ◽  
Raknoi Akararungruangkul
Keyword(s):  
Best Practices ◽  
Current Practice ◽  
Lower Cost ◽  
Time Constraint ◽  
Neighborhood Search ◽  
Routing Problem ◽  
De Algorithm ◽  
Excessive Demand ◽  
Special Case

This paper presents a methodology to solve a special case of the vehicle routing problem (VRP) called the heterogeneous fleets VRP with excessive demand of the vehicle at the pickup points, and the longest time constraint (HFVRP-EXDE-LTC). We developed two metaheuristics—a differential evolution (DE) algorithm and an adaptive large neighborhood search (ALNS)—to solve the problem. These two proposed methods have been designed to effectively solve a special case of VRP. From the computational results, we can see that the proposed heuristics outperformed the best practices that are currently in use. The DE yielded a 9.78% lower cost than that of the current practice (757,250 baht per year), while ALNS generated a 10.89% (906,750 baht per year) lower cost than that of current practice. Comparing the proposed heuristics, ALNS achieved a 1.01% lower cost than that of DE, as ALNS had a better mechanism that was designed to escape from the local optimal.

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