Characteristic problems for a loaded equation of hyperbolic type with a wave operator in the principal part

2018 ◽  
Author(s):  
Anatoly Kh. Attaev
Keyword(s):  
Wave Operator ◽  
Principal Part ◽  
Hyperbolic Type ◽  
Loaded Equation

On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part

2008 ◽  
Vol 15 (3) ◽  
pp. 541-554
Author(s):  
Sergo Kharibegashvili ◽  
Bidzina Midodashvili
Keyword(s):  
Nonlinear Equation ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Wave Operator ◽  
Principal Part ◽  
Boundary Value ◽  
Power Nonlinearity ◽  
Spatial Dimensionality ◽  
Uniqueness Of A Solution

Abstract One boundary value problem for a hyperbolic equation with power nonlinearity and the iterated wave operator in the principal part is considered in a conical domain. Depending on the index of nonlinearity and spatial dimensionality of the equation the question on the existence and uniqueness of a solution of a boundary value problem is investigated. The question as to the absence of a solution of this problem is also considered.

Conversation with a Young Principal (Part VII)

1967 ◽  
Vol 9 (5) ◽  
pp. 34-41
Author(s):  
V. Sukhomlinskii
Keyword(s):  
Principal Part

A new approach to the hydraulic fracture geometric dimensions determination

2017 ◽  
Vol 12 (1) ◽  
pp. 126-134
Author(s):  
A.M. Ilyasov
Keyword(s):  
Exact Solution ◽  
Hydraulic Fracture ◽  
Pressure Gauge ◽  
Hyperbolic Type ◽  
Fluid Injection ◽  
Fracturing Fluid ◽  
New Approach ◽  
Gauge Data ◽  
Bottomhole Pressure ◽  
Half Length

Based on the generalized Perkins-Kern-Nordgren model (PKN) for the development of a hyperbolic type vertical hydraulic fracture, an exact solution is obtained for the hydraulic fracture self-oscillations after terminating the fracturing fluid injection. These oscillations are excited by a rarefaction wave that occurs after the injection is stopped. The obtained solution was used to estimate the height, width and half-length of the hydraulic fracture at the time of stopping the hydraulic fracturing fluid injection based on the bottomhole pressure gauge data.

Patterns of interpredictability and principal parts in Latin verb paradigms: an entropy-based approach

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Matteo Pellegrini
Keyword(s):  
Principal Part ◽  
Quantitative Approach ◽  
Information Theoretic ◽  
Verb Inflection ◽  
Type Frequency ◽  
Principal Parts ◽  
The Impact

AbstractThis paper provides a fully word-based, abstractive analysis of predictability in Latin verb paradigms. After reviewing previous traditional and theoretically grounded accounts of Latin verb inflection, a procedure is outlined where the uncertainty in guessing the content of paradigm cells given knowledge of one or more inflected wordforms is measured by means of the information-theoretic notions of unary and n-ary implicative entropy, respectively, in a quantitative approach that uses the type frequency of alternation patterns between wordforms as an estimate of their probability of application. Entropy computations are performed by using the Qumin toolkit on data taken from the inflected lexicon LatInfLexi. Unary entropy values are used to draw a mapping of the verbal paradigm in zones of full interpredictability, composed of cells that can be inferred from one another with no uncertainty. N-ary entropy values are used to extract categorical and near principal part sets, that allow to fill the rest of the paradigm with little or no uncertainty. Lastly, the issue of the impact of information on the derivational relatedness of lexemes on uncertainty in inflectional predictions is tackled, showing that adding a classification of verbs in derivational families allows for a relevant reduction of entropy, not only for derived verbs, but also for simple ones.

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