scholarly journals On the effective determination of the wave operator from given spectral data in the case of a difference equation corresponding to a Sturm-Liouville differential equation

1970 ◽  
Vol 29 (3) ◽  
pp. 467-497 ◽  
Author(s):  
Lars-Erik Andersson
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Spectral Data ◽  
Wave Operator ◽  
Sturm Liouville

scholarly journals Introduction to Prediction of Operational Efficiency for a Selected Type of a Military Aircraft / Wprowadzenie Do Prognozy Skuteczności Działania Wybranego Typu Wojskowego Statku Powietrznego

2012 ◽  
Vol 21 (1) ◽  
pp. 163-178
Author(s):  
Tomaszek Henryk ◽  
Kaleta Ryszard ◽  
Zieja Mariusz
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Difference Equation ◽  
Operational Efficiency ◽  
Efficiency Factor ◽  
Military Aircraft ◽  
General Outline ◽  
Operational Potential ◽  
Potential Enemy

Abstract The study reveals the general outline for a method of determining the operational efficiency of a military aircraft with respect to destruction of targets held by a potential enemy. The method consists in determination of selected probability factors that define the efficiency of an aircraft’s operation on a potential battlefield. The paper is focused on finding a formula for the mathematical expectation for the number of enemy targets that can be eliminated, where the analytical relationships is determined by means of difference equation that is subsequently transformed into the Fokker-Planck partial differential equation. The solution of that equation represents the function of probable density for the number of destroyable targets. When the function is known it can be then used to determine the efficiency factor related to the optimum (most desired) number of enemy targets that are destroyed. For these probabilities the denominator values are equal to one or the optimum values. The efficiency factor, determined in such a way, seems to be useful for determination of the operational potential demonstrated by a military aircraft.

21,22-Disubstituted 18α,19βH-Ursane Derivatives with Oxabicyclooctane System in Ring E

1993 ◽  
Vol 58 (1) ◽  
pp. 173-190 ◽  
Author(s):  
Eva Klinotová ◽  
Jiří Klinot ◽  
Václav Křeček ◽  
Miloš Buděšínský ◽  
Bohumil Máca
Keyword(s):  
Spectral Data ◽  
Spin Systems ◽  
Coupling Constants ◽  
Complete Analysis ◽  
Nmr Spectrum ◽  
Proton Proton ◽  
H Nmr ◽  
Proton Coupling ◽  
C Nmr

Reaction of 3β-acetoxy-21,22-dioxo-18α,19βH-ursan-28,20β-olide (IIIa) and 20β,28-epoxy-21,22-dioxo-19α,19βH-ursan-3β-yl acetate (IIIb) with diazomethane afforded derivatives XII-XIV with spiroepoxide group in position 21 or 22, which were further converted into hydroxy derivatives XV and XVII. Ethylene ketals VIII-X were also prepared. In connection with the determination of position and configuration of the functional groups at C(21) and C(22), the 1H and 13C NMR spectral data of the prepared compounds are discussed. Complete analysis of two four-spin systems in the 1H NMR spectrum of bisethylenedioxy derivative Xb led to the proton-proton coupling constants from which the structure with two 1,4-dioxane rings condensed with ring E, and their conformation, was derived.

scholarly journals Determination of differential pencils with impulse from interior spectral data

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongxia Guo ◽  
Guangsheng Wei ◽  
Ruoxia Yao
Keyword(s):  
Spectral Data ◽  
Interior Point ◽  
Potential Functions ◽  
Inverse Spectral Problems ◽  
Spectral Problems ◽  
Inverse Spectral ◽  
Differential Pencils ◽  
Second Spectrum

Abstract In this paper, we are concerned with the inverse spectral problems for differential pencils defined on $[0,\pi ]$ [ 0 , π ] with an interior discontinuity. We prove that two potential functions are determined uniquely by one spectrum and a set of values of eigenfunctions at some interior point $b\in (0,\pi )$ b ∈ ( 0 , π ) in the situation of $b=\pi /2$ b = π / 2 and $b\neq \pi /2$ b ≠ π / 2 . For the latter, we need the knowledge of a part of the second spectrum.

Determination of an impulsive diffusion operator from interior spectral data

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 39-45
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Potential Functions ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Impulsive Diffusion

AbstractIn the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions {q_{0}(x)} and {q_{1}(x)} can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.

scholarly journals On partial fractional Sturm–Liouville equation and inclusion

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zohreh Zeinalabedini Charandabi ◽  
Hakimeh Mohammadi ◽  
Shahram Rezapour ◽  
Hashem Parvaneh Masiha
Keyword(s):  
Differential Equation ◽  
Liouville Equation ◽  
Existence Of Solutions ◽  
Liouville Problem ◽  
Existence Of A Solution ◽  
Contractive Mappings ◽  
Sturm Liouville

AbstractThe Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence of a solution for partial fractional Sturm–Liouville equation by using the α-ψ-contractive mappings. Also, we give an illustrative example. By using the α-ψ-multifunctions, we prove the existence of solutions for inclusion version of the partial fractional Sturm–Liouville problem. Finally by providing another example and some figures, we try to illustrate the related inclusion result.

scholarly journals p-adic confluence of q-difference equations

2008 ◽  
Vol 144 (4) ◽  
pp. 867-919 ◽  
Author(s):  
Andrea Pulita
Keyword(s):  
Differential Equation ◽  
Difference Equation ◽  
Differential Equations ◽  
Difference Equations ◽  
Root Of Unity

AbstractWe develop the theory of p-adic confluence of q-difference equations. The main result is the fact that, in the p-adic framework, a function is a (Taylor) solution of a differential equation if and only if it is a solution of a q-difference equation. This fact implies an equivalence, called confluence, between the category of differential equations and those of q-difference equations. We develop this theory by introducing a category of sheaves on the disk D−(1,1), for which the stalk at 1 is a differential equation, the stalk at q isa q-difference equation if q is not a root of unity, and the stalk at a root of unity ξ is a mixed object, formed by a differential equation and an action of σξ.

Synthesis of 4-(3-coumarinyl)-3-benzyl-4-thiazolin-2-one 4-methylbenzylidenehydrazone and determination of the isomeric structure by X-ray analysis

2003 ◽  
Vol 218 (12) ◽  
Author(s):  
Süheyla Özbey ◽  
Nilgün Karalı ◽  
Aysel Gürsoy
Keyword(s):  
Single Crystal ◽  
Diffraction Analysis ◽  
Spectral Data ◽  
X Ray Diffraction ◽  
X Ray ◽  
Isomeric Structure ◽  
Elemental Analyses

AbstractIn this study 4-(3-coumarinyl)-3-benzyl-4-thi azolin-2-one 4-methylbenzylidenehydrazone 3 was synthesised. An independent proof of the thiazolylhydrazone structure of 3 was achieved by single crystal X-ray diffraction analysis. Elemental analyses and spectral data (IR,

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

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