Wyniki wyszukiwania - BazTech

1

On the blowing up solutions of the 4-d general q-Kuramoto-Sivashinsky equation with exponentially “dominated” nonlinearity and singular weight

Baraket Sami, Mahdaoui Safia, Ouni Taieb

Opuscula Mathematica

|

2023

|

Vol. 43, no. 1

5--18

EN

Let Ω be a bounded domain in R4 with smooth boundary and let x1, x2, . . . , xm be m-points in Ω. We are concerned with the problem [formula], where the principal term is the bi-Laplacian operator, H(x, u, Dku) is a functional which grows with respect to Du at most like |Du|q, 1 ≤ q ≤ 4, f : Ω → [0,+∞[ is a smooth function satisfying f(pi) > 0 for any i = 1, . . . , n, αi are positives numbers and g : R → [0,+∞[ satisfy |g(u)| ≤ ceu. In this paper, we give sufficient conditions for existence of a family of positive weak solutions (uρ) ρ>0 in Ω under Navier boundary conditions u = Δu = 0 on ∂Ω. The solutions we constructed are singular as the parameters ρ tends to 0, when the set of concentration S = {x1, . . . , xm} ⊂ Ω and the set Λ := {p1, . . . , pn} ⊂ Ω are not necessarily disjoint. The proof is mainly based on nonlinear domain decomposition method.

2

The gradient and the divergence for vector-valued forms

Klekot Agnieszka, Pierzchalski Antoni

Journal of Applied Mathematics and Computational Mechanics

|

2023

|

Vol. 22, nr 1

31--45

EN

On a Riemannian manifold, two differential operators: the gradient and the divergence are defined and investigated in the bundle of alternating differential forms of any degree with values in a vector bundle. Several algebraic, analytic and geometric properties of the two operators are derived. The vector character of the gradient on forms turns out to be a source of possible applications.

3

Zastosowanie rachunku niecałkowitego rzędu w obliczeniach gradientu pola skalarnego

Włodarczyk Maciej, Zawadzki Andrzej, Różowicz Sebastian

Przegląd Elektrotechniczny

|

2022

|

R. 98, nr 12

114--117

PL

W artykule przedstawiono zastosowanie pochodnych ułamkowego rzędu do wyznaczania gradientu pola skalarnego, także przy zmianie układu współrzędnych. W naszych obliczeniach natężenie pola elektrycznego ładunku punktowego zostało wyznaczone na podstawie potencjału pola elektrycznego. Zbadano niektóre własności wyznaczonego gradientu.

EN

The paper presents the use of fractional-order derivatives for determining the scalar field gradient, also for the change of the coordinate system. In our calculations the electric field strength of the point charge was determined on the basis of the electric field potential. Some properties of the determined gradient were examined.

4

Własności pochodnej kierunkowej w zadaniach

Łobos Ewa

MINUT Matematyka i Informatyka na Uczelniach Technicznych

|

2022

|

Nr 4

61-69

PL

Artykuł zawiera kilka ciekawych i niebanalnych (co jest oczywiście subiektywną opinią autorki) zadań związanych z pochodną kierunkową. Jest przeznaczony dla studentów, którzy chcieliby utrwalić swoją wiedzę w tym zakresie. Zadania nie się trudne, ale wymagają czegoś więcej niż sprawdzenie założeń i podstawienie do wzoru. W pracy podano szczegółowe rozwiązania tych zadań. Na końcu artykułu Czytelnik znajdzie także zadania do samodzielnej pracy.

5

O pochodnej kierunkowej i gradiencie

Łobos Ewa

MINUT Matematyka i Informatyka na Uczelniach Technicznych

|

2022

|

Nr 4

47-60

PL

Celem tego artykułu jest przybliżenie Czytelnikowi pojęcia pochodnej kierunkowej. Podano definicję i interpretację pochodnej kierunkowej oraz najważniejsze twierdzenia umożliwiające jej obliczanie. Praca zawiera przykłady ilustrujące przytoczone twierdzenia oraz przykłady obliczania pochodnej kierunkowej bezpośrednio z definicji. Czytelnik znajdzie także propozycje zadań do samodzielnego rozwiązania.

6

Geometric approach to machine exploitation efficiency : modelling and assessment

Loska Andrzej, Paszkowski Waldemar

Eksploatacja i Niezawodność

|

2022

|

Vol. 24, no. 1

114--122

EN

This article presents a new approach to the exploitation assessment of machines and devices. A key aspect of this approach is the construction of the assessment model based on the geometric representation of measures associated with each other, which covers the full specifics of the exploitation process. This approach is successfully implemented by the Overall Equipment Effectiveness (OEE) model, which is fully susceptible to the geometric modelling process due to the three-way system of assessed exploitation aspects. The result of this approach is the vectored OEE model and its interpretation in terms of time series of changes in values of components. Methods of determining vector calculus measures were developed, including the second-order tensor and gradient. This is the subject of the variability of the reliability conditions of machines or production processes. It allows for the realisation of an exploitation assessment based on dynamic changes in the values of their components in the time domain. This is a significant difference to the classical static approach to such an assessment. The developed new geometric OEE model was confirmed by verification tests using the LabView software, based on two parallel data sets obtained with analytical and simulation methods using the FlexSim software.

7

Some recent results on singular p-Laplacian equations

Guarnotta Umberto, Livrea Roberto, Marano Salvatore A.

Demonstratio Mathematica

|

2022

|

Vol. 55, nr 1

416--428

EN

A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.

8

New estimate for the curvature of an order-convex set and related questions

Ramazanov Ali B.

Control and Cybernetics

|

2020

|

Vol. 49, No. 2

233--240

EN

It is well known that in discrete optimization problems, gradient (local) algorithms do not always guarantee an optimal solution. Therefore, the problem arises of finding the accuracy of the gradient algorithm. This is a fairly well-known problem and numerous publications have been devoted to it. In establishing accuracy, various approaches are used. One of these approaches is to obtain guaranteed estimates of the accuracy of the gradient algorithm in terms of the curvature of the admissible domain. With this approach, it is required to find the curvatures of the admissible region. Since finding the exact value of curvature is a difficult problem to solve, curvature estimates in terms of more or less simply calculated parameters of the problem are relevant. A new improved bound for the curvature of an order-convex set is found and is presented in this paper in terms of the steepness and parameters of strict convexity of the function.

9

Multichannel antileakage least squares spectral analysis for seismic data regularization beyond aliasing

Ghaderpour Ebrahim

Acta Geophysica

|

2019

|

Vol. 67, no. 5

1349--1363

EN

The antileakage least-squares spectral analysis is a new method of regularizing irregularly spaced data series. This method mitigates the spectral leakages in the least-squares spectrum caused by non-orthogonality of the sinusoidal basis functions on irregularly spaced series, and it is robust when data series are wide-sense stationary. An appropriate windowing technique can be applied to adapt this method to non-stationary data series. When data series present mild aliasing, this method can efectively regularize the data series; however, additional information or assumption is needed when the data series is coarsely sampled. In this paper, we show how to incorporate the spatial gradients of the data series into the method to regularize data series presenting severe aliasing and show its robust performance on synthetic and marine seismic data examples.

10

Image Inpainting with Gradient Attention

Sadowski Michał, Grzegorczyk Aleksandra

Schedae Informaticae

|

2018

|

Vol. 27

81--91

EN

We present a novel modification of context encoder loss function, which results in more accurate and plausible inpainting. For this purpose, we introduce gradient attention loss component of loss function, to suppress the common problem of inconsistency in shapes and edges between the inpainted region and its context. To this end, the mean absolute error is computed not only for the input and output images, but also for their derivatives. Therefore, model concentrates on areas with larger gradient, which are crucial for accurate reconstruction. The positive effects on inpainting results are observed both for fully-connected and fully-convolutional models tested on MNIST and CelebA datasets.

11

Gradient copolymers from aromatic and aliphatic 2-oxazolines as promising biomedical materials

Kronek J., Petrenćíková N., Kroneková Z., Datta S., Jancura D.

Engineering of Biomaterials

|

2018

|

Vol. 21, no. 148

96

12

3D joint inversion of Gradient and Mise-à-la-Masse borehole IP/Resistivity data and its application to magmatic sulfide mineral deposit exploration

Wondimu H. D., Mammo T., Webster B.

Acta Geophysica

|

2018

|

Vol. 66, no. 5

1031--1045

EN

Gradient and Mise-à-la-Masse IP/Resistivity surveys were conducted on a group of 19 boreholes in Eagle’s Nest, Eagle One magmatic sulfide deposit in northern Ontario, Canada. The surveys were conducted as a follow-up to the many drilled boreholes, some of which missed the target. The surveys were intended to map the distribution of the ore mineralization, outline the deposit hosted by mafic and ultramafic rocks and then guide the drilling of new boreholes. Joint Gradient and Mise-à-la-Masse data inversion produced 3D chargeability and conductivity models. The inverted 3D models in turn help delineate the outline of the mineralized zone, and determine the shape, size, strength and economic viability of the deposit. The Gradient array determined the direction of the mineralization with respect to the boreholes, and the Mise-à-la-Masse array examined the highly conductive subsurface bodies and their surroundings. The mapped ore zone shows close similarity to the 0.5 Cu% and 1.05 Ni% iso-surfaces that are produced from core assay result confirming the reliability of the results obtained in this study.

13

Some differential operators in the symmetric bundle

Kimaczyńska A.

Journal of Applied Mathematics and Computational Mechanics

|

2017

|

Vol. 16, nr 3

27--36

EN

Some natural differential operators in the bundles of symmetric tensors and symmetric tensors with values in the tangent bundle are investigated. Applications in geometry, physics and tomography are also reviewed.

14

A Hydrophysical Analysis of Urban Surface Runoff, Channel Characteristics, and the Incidence of Flood and Erosion Over the Calabar Drainage Area, Nigeria.

Ugbong I. A., Budagov I. V.

Journal of Ecological Engineering

|

2016

|

Vol. 17, nr 3

30--40

EN

Hydro-physical processes operating in the Calabar drainage area were analyzed by estimating the volume of surface runoff carried in each basin and sub-basin, using field measurements of flow velocities in conjunction with the “Rational Method” mathematical model proposed by civil and environmental engineers. It was found that run-off flow is affected by at least three factors which either produce floods or erosion conditions. The factors include size of catchment areas, gradient and lengths of flow channels. The Multiple Regression statistic was used to test these relationships. The results showed a strong statistical correlation among these variables, as well as between these variables and flow characteristics. It was found that for all the basins, runoff volume increased with increasing surface area of the catchment; just as areas with lower elevations register higher flow volume accompanied by flooding; with a reversed condition in higher ground where higher velocities are found with resultant erosion conditions. Also channels with considerable lengths receive higher flows along their courses downstream, and thus produce floods. It was therefore, recommended that in addition to the six major drainage channels recommended for the area, each channel and each segment of a channel should be determined by its gradient, drainage area, length of flow channel.

15

Correction of Hydrological and Oceanic Effects from GRACE Data by Combination of the Steric Sea Level, Altimetry Data and GLDAS Model

Fatolazadeh F., Voosoghi B, Raoofian Naeeni M.

Acta Geophysica

|

2016

|

Vol. 64, no. 4

1193--1210

EN

In this study, a scheme to estimate oceanic and hydrological effects in the GRACE (Gravity Recovery and Climate Experiment) data is presented. The aim is to reveal tectonic signals for the case of the Sumatra earthquake on 26 December 2004. The variations of hydrological and oceanic effects are estimated with the aid of data set of GRACE, altimetry, World Ocean Atlas, and the GLDAS model for a period of January 2003 to December 2006. The time series of computed gravity changes over Sumatra region show some correlations to the deformation resulting from the earthquake occurred in December 2004. The maximum and minimum impacts of hydrological and oceanic effects on gravity changes are about 3 μGal in radial direction and –5 μGal in northward direction. The maximum and minimum amounts of gravitational gradient changes after the correction are 0.2 and –0.25 mE, which indicates the significant influences of hydrological and oceanic sources on the desired signal.

16

Kinetyka zużycia galwanicznych kompozytowych powłok w czasie tarcia

Wajs E.

Logistyka

|

2015

|

nr 4

6403--6410, CD 2

PL

W artykule przedstawiono kinetykę zużycia kompozytowych gradientowych powłok, w których podstawowym typem struktury są warstwowe, matrycowe wtrącenia, poddane obciążeniom statycznym i dynamicznym, wywołanych siłami tarcia ślizgowego lub tocznego. Pokazano, że powłoki gradientowego typu z nano kompozytową osnową i równomiernie rozłożonymi w niej makro wtrąceniami, cechują się wysoką odpornością na zużycie. Optymalną, dla stykających się powierzchni poddanym znacznym obciążeniom przy tarciu ślizgowym, jest dyspersyjnie umocniona osnowa, , zawierająca wtrącenia związane z metaliczną osnową i przejściową strefą dyfuzyjnego współdziałania.

EN

It was established that coatings of the gradient type with a high carrying capacity has enough wear resistance. An optical high-loaded sliding friction couple is a dispersively strengthened or diffusively alloyed matrix deposited over a directedly crystallized columnlike eutectic layer on an under-layer containing macro inclusions connected with the metal matrix and substrate through a transition zone of diffusive interaction.

17

Gradient trajectories for plane singular metrics I : oscillating trajectories

Grandjean V.

Demonstratio Mathematica

|

2014

|

Vol. 47, nr 1

69--78

EN

In this short note, we construct an example of a real plane analytic singular metric, degenerating only at the origin, such that any gradient trajectory (respectively to this singular metric) of some well chosen function spirals around the origin. The inversion mapping carries this example into an example of a gradient spiraling dynamics at infinity.

18

Ecological boundaries at different scales: testing the moving split window analysis using artificial and field data

Erdős L., Bátori Z., Morschhauser T., Körmöczi L.

Polish Journal of Ecology

|

2013

|

Vol. 61, nr 2

319--328

EN

Scale-dependency is one of the well-known features of ecological boundaries. Unfortunately, there are relatively few case studies analysing boundaries of different scales. Moreover, properties of moving split window (MSW) technique, a method potentially suitable for examining boundaries at several spatial scales, are not fully understood. In this study, we used artificial data sets to test the capacities and limitations of the MSW method. We also applied field data from the Mecsek Mts (Hungary) (611 m a.s.l.) in order to reveal possible boundaries at different scales and to contribute to the knowledge on vegetation pattern of mountain areas. We found that one should apply several window-widths when using MSW, since this is the only way to detect and differentiate between boundaries of different scales. Our study revealed the vegetation pattern of Mt Tubes: there is a series of continuously intergrading mesic communities on the northern slope, while the southern slope is occupied by a mosaic of different xeric communities. In this pattern, boundaries of two different scales have been identified. We conclude that MSW could effectively be used in similar mountain regions to analyse herb layer vegetation patterns and boundaries.

19

Mechanical properties of a-C:H/Ti layers on prosthodontic CoCr and NiCr alloys

Szymański W., Batory D., Cłapa M., Klimek L.

Engineering of Biomaterials

|

2009

|

Vol. 12, no. 85

2--5

EN

Co-Cr and Ni-Cr alloys are widely used in dental implants production. However, there is a risk connected with application of this kind of materials like allergy and methalosis caused by Cr, Ni ions, very dangerous for patients’ health and life. Moreover metal ions released into human body can affect inflammation of the surrounding tissue. Biomaterials’ surface treatment by the deposition of diamond-like carbon films can noticeably improve the corrosion and mechanical features. Widely discussed in world’s literature problems with adhesion of DLC layers can be solved by the deposition of gradient a-C:H/Ti layer. Due to that, it is possible to manufacture thick and well adherent carbon layer on the implant’s surface which will constitute a very good protection against wear and corrosion. Our goal was to evaluate the mechanical properties of a-C:H/Ti layers deposited on CoCr and NiCr alloys in hybrid deposition system RF PACVD/MSand to find the influence of layer thickness on the selected properties. As the result of the investigation it was noticed that deposition of a-C:H/Ti layer improves the mechanical properties of CoCr and NiCr alloys. High hardness and good adhesion of gradient carbon layers makes them a very perspective material for this kind of applications.

20

Analiza wytrzymałościowa i odkształceniowa biomateriałów gradientowych przeznaczonych na implanty

Migacz K., Chłopek J.

Engineering of Biomaterials

|

2009

|

Vol. 12, no. 89-91

175--178

PL

W pracy autorzy przedstawiają analizę wytrzymałościową i odkształceniową kompozytów gradientowych z kontrolowaną zmianą modułu Younga w warunkach symulowanego środowiska biologicznego. Zaprojektowane przy pomocy MES pięciowarstwowe kompozyty z PSU/CF 1D z gradientem otrzymanym poprzez zmianę udziału procentowego włókien (10, 15, 20, 30, 40%) po wstępnych testach wytrzymałościowych i odkształceniowych zostały umieszczone w płynie Ringera pod działaniem stałego obciążenia siłą P=1200N przez okres 56 dni. Co 14 dni wykonywano pomiary ultradźwiękowe, po okresie inkubacji próbki poddano badaniom wytrzymałościowym do 5000 N. Wyniki pomiarów wykazują przydatność materiału gradientowego PSU/CF 1D jako implantów dokręgosłupowych ze względu na ich dobrze dopasowany moduł Younga i odkształcalność do naturalnego krążka międzykręgowego człowieka. W kolejnym etapie badań zostanie wykonana analiza zmęczeniowa materiałów w celu określenia ich trwałości.

EN

In this article strength and strain analysis of gradient composites with controlled change of Young’s modulus in simulated biological environment was presented. Polysulfon/carbon fibers (PSU/CF) 1D composites with gradient of the content of PSU to CF (10, 15, 20, 30, 40 wt% of CF), built up of 5 layers were designed by using FEM. After preliminary strength and strain tests they were incubated in Ringer’s under the static load P=1200 N solution for 56 days. Ultrasonic measurements were made every 14 days. After incubation samples mechanical strength was tested with the load up to 5000 N. The obtained results show suitability of PSU/CF 1D gradient material for spine implants because of well – matched Young’s modulus and deformability to natural human intervertebral disc. As a next step of the research fatigue testing analysis will be done, in order to obtain materials’ durability.