scholarly journals G˚arding Cones and Bellman Equations in the Theory of Hessian Operators and Equations

2017 ◽  
Vol 63 (4) ◽  
pp. 615-626
Author(s):  
N M Ivochkina ◽  
N V Filimonenkova
Keyword(s):  
Partial Differential Equations ◽  
Differential Operators ◽  
Comparison Theorems ◽  
Symmetric Matrices ◽  
New Approach ◽  
Bellman Equations ◽  
Nonlinear Differential Operators ◽  
Algebraic Properties ◽  
New Type ◽  
Continue Investigation

In this work, we continue investigation of algebraic properties of G˚arding cones in the space of symmetric matrices. Based on this theory, we propose a new approach to study of fully nonlinear differential operators and second-order partial differential equations. We prove new-type comparison theorems for evolution Hessian operators and establish a relation between Hessian and Bellman equations.

scholarly journals Cryogenic Exfoliation of 2D Stanene Nanosheets for Cancer Theranostics

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Jiang Ouyang ◽  
Ling Zhang ◽  
Leijiao Li ◽  
Wei Chen ◽  
Zhongmin Tang ◽  
...  
Keyword(s):  
Biomedical Applications ◽  
Density Functional ◽  
Biomedical Application ◽  
Density Functional Theory Calculations ◽  
Free Electrons ◽  
Functional Theory ◽  
New Approach ◽  
New Type ◽  
Average Size ◽  
Cancer Theranostics

Abstract Stanene (Sn)-based materials have been extensively applied in industrial production and daily life, but their potential biomedical application remains largely unexplored, which is due to the absence of the appropriate and effective methods for fabricating Sn-based biomaterials. Herein, we explored a new approach combining cryogenic exfoliation and liquid-phase exfoliation to successfully manufacture two-dimensional (2D) Sn nanosheets (SnNSs). The obtained SnNSs exhibited a typical sheet-like structure with an average size of ~ 100 nm and a thickness of ~ 5.1 nm. After PEGylation, the resulting PEGylated SnNSs (SnNSs@PEG) exhibited good stability, superior biocompatibility, and excellent photothermal performance, which could serve as robust photothermal agents for multi-modal imaging (fluorescence/photoacoustic/photothermal imaging)-guided photothermal elimination of cancer. Furthermore, we also used first-principles density functional theory calculations to investigate the photothermal mechanism of SnNSs, revealing that the free electrons in upper and lower layers of SnNSs contribute to the conversion of the photo to thermal. This work not only introduces a new approach to fabricate 2D SnNSs but also establishes the SnNSs-based nanomedicines for photonic cancer theranostics. This new type of SnNSs with great potential in the field of nanomedicines may spur a wave of developing Sn-based biological materials to benefit biomedical applications.

On invariant subspaces for nonlinear finite-difference operators

1998 ◽  
Vol 128 (6) ◽  
pp. 1293-1308 ◽  
Author(s):  
Victor A. Galaktionov
Keyword(s):  
Finite Difference ◽  
Differential Operators ◽  
Invariant Subspaces ◽  
Reaction Diffusion ◽  
Difference Operators ◽  
Diffusion Type ◽  
Nonlinear Differential Operators ◽  
Discrete Operators ◽  
Spatial Discretisation ◽  
Lower Dimensional

We study linear subspaces invariant under discrete operators corresponding to finitedifference approximations of differential operators with polynomial nonlinearities. In several cases, we establish a certain structural stability of invariant subspaces and sets of nonlinear differential operators of reaction–diffusion type with respect to their spatial discretisation. The corresponding lower-dimensional reductions of the finite-difference solutions on the invariant subspaces are constructed.

scholarly journals The Extension of the Physical and Stochastic Problems to Space-Time-Fractional Differential Equations

2021 ◽  
Vol 2090 (1) ◽  
pp. 012031
Author(s):  
E.A. Abdel-Rehim
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Differential Operators ◽  
Space Time ◽  
Partial Differential ◽  
Stochastic Problems ◽  
Fractional Differential ◽  
Fractional Differential Operators ◽  
Time Fractional Differential Equations

Abstract The fractional calculus gains wide applications nowadays in all fields. The implementation of the fractional differential operators on the partial differential equations make it more reality. The space-time-fractional differential equations mathematically model physical, biological, medical, etc., and their solutions explain the real life problems more than the classical partial differential equations. Some new published papers on this field made many treatments and approximations to the fractional differential operators making them loose their physical and mathematical meanings. In this paper, I answer the question: why do we need the fractional operators?. I give brief notes on some important fractional differential operators and their Grünwald-Letnikov schemes. I implement the Caputo time fractional operator and the Riesz-Feller operator on some physical and stochastic problems. I give some numerical results to some physical models to show the efficiency of the Grünwald-Letnikov scheme and its shifted formulae. MSC 2010: Primary 26A33, Secondary 45K05, 60J60, 44A10, 42A38, 60G50, 65N06, 47G30,80-99

scholarly journals Scientia est potentia

2009 ◽  
pp. 43-60
Author(s):  
Ülo Kaevats
Keyword(s):  
Modern Science ◽  
New Approach ◽  
Natural Laws ◽  
Modern Times ◽  
Natural Objects ◽  
Deductive Method ◽  
New Type ◽  
The Subject ◽  
Understanding Of Science ◽  
Object Of Study

Oma algses mitmetähenduslikkuses on see F. Baconi aforism kõige tihendatum tõdemus, mis tõmbab olemusliku eraldusjoone ühelt poolt antiikse ja keskaegse ning teisalt uusaegse arusaama vahele teadusest ja teadusteadmisest. Artiklis püüab autor anda võimaluste piires tervikpildi uusaja teaduse industriaalselt (tehnoloogiliselt) orienteeritud teadmistüübi tekkimisest. Uusaja teaduse kujunemiseks vajaliku pöörde maailmavaateliste eeldustena tuleb käsitleda: (1) põhimõtteliselt uut subjekti ja objekti käsitust; (2) täiesti uut väärtusruumi, uut teaduse ideoloogiat (ilmalikkus, kriitiline vaim, tõesus ja praktiline kasulikkus); (3) tunnetuslaadi muutust — kontemplatsioonilt interventsioonile, kvaliteedi kirjeldamiselt kvantiteedi uurimisele; (4) looduse käsitlemist Kosmose asemel seaduspäraselt korrastatud objektide “väljana”. Uue tunnetusstiili — empiirilise ja teoreetilise tunnetuse kokkuviimine, hüpoteetilis-deduktiivse metodoloogia kujundamine Galilei poolt, abstraktse ja sünteetilis-tekstilise loomuga spekulatsiooni asendumine uurimisobjekti ehituse, korrapära ja põhjuslikkuse objektiivse analüüsiga, universaalsete loodusseaduste doktriini kujunemine jms—kujunemine konstitueeris uut tüüpi teadmise. Teadmise kui nähtava maailma piltkoopia asemele luuakse teadmine kui loodusobjektide seaduspära analüütiline rekonstruktsioon. See on vormiltmatemaatiline, päritolult eksperimentaalne ning loodusobjektide kontrollimisele ja ümbertegemisele suunatud nn valdamisteadmine.This F. Bacon's aphorism in its original ambiguity is the most condensed belief that draws a distinctive essential line between ancient and medieval understanding of science and scientific knowledge on one hand and modern understanding on the other. The author aims at providing, as far as possible, an integral overview of emerging of the industrially (technologically) orientated type of knowledge of modern times. Ideological/philosophical preconditions of the change necessary for emerging of modern science are: (1) a fundamentally new approach to the subject and object; (2) a completely new system of values, a new ideology of science (secularity, critical spirit, trueness and utilitarianism); (3) a change in manner of cognizance - from contemplation to intervention, from describing quality to studying quantity; (4) treating nature as a naturally organised "field" of objects instead of the Cosmos. Emerging of a new style of cognizance - bringing together of empirical and theoretical cognition, the devise of the hypothetical-deductive method by Galilei, replacement of speculations abstract and synthetic-textual in nature with objective study of the structure, regularity and causality of the object of study, establishment of the doctrine of universal natural laws etc - constituted a new type of knowledge. Knowledge as a copy of the visible world is replaced by knowledge as an analytical reconstruction of the regularity of natural objects. It is so-called dispositive knowledge, morphologically mathematical, originally experimental and aimed at control and alteration of natural objects.

scholarly journals AILU FOR HELMHOLTZ PROBLEMS: A NEW PRECONDITIONER BASED ON THE ANALYTIC PARABOLIC FACTORIZATION

2001 ◽  
Vol 09 (04) ◽  
pp. 1499-1506 ◽  
Author(s):  
MARTIN J. GANDER ◽  
FRÉDÉRIC NATAF
Keyword(s):  
Numerical Experiments ◽  
New Approach ◽  
New Type

We investigate a new type of preconditioner which is based on the analytic factorization of the operator into two parabolic factors. Approximate analytic factorizations lead to new block ILU preconditioners. We analyze the preconditioner at the continuous level where it is possible to optimize its performance. Numerical experiments illustrate the effectiveness of the new approach.

Regularity Estimates for Nondivergence Parabolic Equations on Generalized Orlicz Spaces

2020 ◽  
Author(s):  
The Anh Bui
Keyword(s):  
Parabolic Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Harmonic Analysis ◽  
Parabolic Equations ◽  
Orlicz Spaces ◽  
Representation Theorems ◽  
New Approach ◽  
Analysis Techniques ◽  
Regularity Estimates

Abstract In this paper, by using a new approach, we prove regularity estimates for the solution to the nondivergence parabolic equation on generalized Orlicz spaces. Our approach can be viewed as a combination of representation theorems in partial differential equations and harmonic analysis techniques.

Part Accuracy Management by Topological Mapping of Deviations

2016 ◽  
Vol 859 ◽  
pp. 210-216
Author(s):  
Gabriel Frumuşanu ◽  
Alexandru Epureanu
Keyword(s):  
Geometrical Model ◽  
Synthetic Approach ◽  
Concrete Case ◽  
Topological Map ◽  
New Approach ◽  
Part Geometry ◽  
Real Geometry ◽  
Geometric Deviations ◽  
New Type ◽  
Modern Manufacturing

Despite modern manufacturing processes are characterized by a continuously increasing accuracy, geometric deviations inherently appear on every manufactured part so, for quality-aware companies, it is essential to control and to manage them. This paper introduces a new type of part geometrical model, namely the part topological map, in connection with a new approach in part accuracy management. The part topological map enables a global analytical & synthetic approach of the problems related to tolerancing domain and a generalization of the “part accuracy” concept. The part geometry is seen as a stand-alone ensemble of surfaces dimensionally related, unitary and with its own shape, dimensions and position. The real geometry has also a global, unitary deviation, characterized through deviation features. Each component surface is represented in a particular manner, unrolled, while its deviation features are assessed by using series expansion of the deviations corresponding to a cloud of measured points. A method for effectively realizing the topological map of a part deviation and a numerical exercise to illustrate the method application in a concrete case are also included.

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