scholarly journals On the Stability of Kalman--Bucy Diffusion Processes

2017 ◽  
Vol 55 (6) ◽  
pp. 4015-4047 ◽  
Author(s):  
Adrian N. Bishop ◽  
Pierre Del Moral
2019 ◽  
Vol 17 (1) ◽  
pp. 1490-1502 ◽  
Author(s):  
Jia-Bao Liu ◽  
Muhammad Javaid ◽  
Mohsin Raza ◽  
Naeem Saleem

Abstract The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.


2020 ◽  
Vol 178 (3-4) ◽  
pp. 1125-1172
Author(s):  
Julio Backhoff-Veraguas ◽  
Daniel Bartl ◽  
Mathias Beiglböck ◽  
Manu Eder

Abstract A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion–Nadal and Talay introduce a version of the Wasserstein distance between the laws of diffusion processes. Pflug and Pichler consider the nested distance (and the weak nested topology) to obtain continuity of stochastic multistage programming problems. These distances can be seen as a symmetrization of Lassalle’s causal transport problem, but there are also further natural ways to derive a topology from causal transport. Our main result is that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover we show that this ‘weak adapted topology’ is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions.


2008 ◽  
Vol 19 (04) ◽  
pp. 569-581 ◽  
Author(s):  
DAMIÁN H. ZANETTE

A formulation of bit-string models of language evolution, based on differential equations for the population speaking each language, is introduced and preliminarily studied. Connections with replicator dynamics and diffusion processes are pointed out. The stability of the dominance state, where most of the population speaks a single language, is analyzed within a mean-field-like approximation, while the homogeneous state, where the population is evenly distributed among languages, can be studied. This analysis discloses the existence of a bistability region, where dominance coexists with homogeneity as possible asymptotic states. Numerical resolution of the differential system validates these findings.


Author(s):  
Лилия Александровна Пасечник ◽  
Ирина Сергеевна Медянкина ◽  
Светлана Александровна Бибанаева ◽  
Сергей Павлович Яценко

Предложены методы модификации красных шламов (КШ) обработкой соляной кислотой и карбонизацией с получением сорбционных материалов, пригодных для извлечения металлов из кислых растворов. Модификация КШ карбонизацией способствует увеличению площади и объема пор в карбонизированном шламе (КШК), что привело к более высокой сорбционной емкости до 246 мг Cu /г, при одновременной нейтрализации сернокислого медьсодержащего раствора с 1,5 до 4,5 единиц pH . Кислотная обработка приводит к меньшим положительным эффектам по извлечению меди. Кинетика сорбции описывается уравнениями как псевдо-первого порядка ( R > 0,96 ), так и псевдо-второго ( R > 0,98), определяя равнозначные вклады в общую скорость процесса стадий массопереноса и взаимодействия ионов. При изучении механизма установлено, что поверхностные диффузионные процессы на границе «твердое - жидкое» переходят в массоперенос ионов Cu и химическое взаимодействие с функциональными группами на поверхности и внутри частиц модифицированных шламов. Для исходного шлама эти процессы практически эквивалентны. Десорбция меди водой и раствором этилендиаминтетрауксусной кислотой (ЭДТА) показала, что прочность связей в структуре КШК- Cu и устойчивость поверхностных тройных комплексов Cu -ЭДТА-КШК оказывается выше, чем Cu -ЭДТА-КШ. Показана перспектива создания сорбционных материалов на основе промышленных отходов, в частности щелочных красных шламов, и их применение для поглощения токсичных металлов из кислых сточных вод с взаимной нейтрализацией и утилизацией разных видов техногенных отходов металлургических производств -твердых, газообразных и жидких. Methods for modification red mud (RM) by treatment with hydrochloric acid and by carbonization to obtain sorption materials for extracting metals from acidic solutions are proposed. Modification of the RM by carbonation increases the area and volume of pores in the carbonized red mud (CRM), that leads to a higher sorption capacity up to 246 mg/g with simultaneously neutralization of the copper solution from 1,5 to 4,5 pH . The acid treatment leads to less positive effects on the extraction of copper. The sorption kinetics is described by both pseudo-first-order (R >0 ,96) and pseudo-second-order (R > 0,98) equations, which determine the equivalent contributions to the overall speed of the process of the mass transfer and the ion interaction stages. A mechanism was studied and it was found that surface diffusion processes at the «solid-liquid» interface turn into the mass transfer of Cu ions and chemical interaction with functional groups on the surface and inside the particles of modified muds. For the initial mud, these processes are almost equivalent. Desorption of copper with water and a solution of ethylenediaminetetraacetic acid (EDTA) has shown that the strength of bonds in the structure of CRM- Cu and the stability of surface triple complexes Cu -EDTA-CRM are higher than for Cu -EDTA-RM. The potential have been demonstrated of creating sorption materials by used industrial waste, in particular alkaline red slurries, and their applications for the absorption of toxic metals from acidic wastewater for mutual neutralization and utilization of industrial waste from metallurgical industries - solid, gaseous and liquid.


2006 ◽  
Vol 965 ◽  
Author(s):  
Silvia Janietz ◽  
Udom Assawapirom ◽  
Dessislava Sainova

ABSTRACTHere we present a concept to improve the field effect transistor performance of P3HT in terms of threshold voltage stability as well as the stability in ambient atmosphere by introducing a strong acceptor dopant in the main polymer chain. In our concept the direct introduction of the acceptor dopant in the polymer main chain ensures the strucural stability against diffusion processes. P3HTs with different contents of acceptor molecules which are fixed linked in the main chain of the polymer , have been synthesized using the McCullough Grignard metathesis method. As acceptor unit has been integrated tetrafluorbenzene (TFB). The introduced dopant amount has been varied in order to obtain an optimum between the processability of the polymers and the resultant transistor performance.Compared to the p-type semionducting polymers the n-type organic materials are markedly less developed. Recently an interesting solution to this task has been proposed in the form of a conjugated ladder-type poly (benzo-bisimidazobenzo-phenanthroline) (BBL) showing either ambipolar or n-type field effect properties dependent upon the sample preparation and processing. However this rigid-chain ladder polymer is not soluble in the common organic solvents resulting in a rather complicated technological transfer. We report the significant improvement of the BBL-processing utilizing aqueous colloidal dispersions and their OFET-application. The resultant devices demonstrate ambipolar electronic transport with charge carrier mobilities in the range of 10−5 cm2/Vs without specific optimization procedures..


2014 ◽  
Vol 59 (8) ◽  
pp. 1238-1241 ◽  
Author(s):  
S. N. Grigor’ev ◽  
E. E. Karpova ◽  
V. B. Oshurko

Author(s):  
Sabir Umarov

AbstractIn this paper continuous time and discrete random walk models approximating diffusion processes associated with time-fractional and spacedistributed order differential equations are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is the inverse to a Levy’s stable subordinator with the stability index β ∈ (0, 1). In the paper the convergence of modeled continuous time and discrete random walks to time-changed processes associated with distributed order fractional diffusion equations are proved using an analytic method.


2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Guilherme Ferraz de Arruda ◽  
Michele Tizzani ◽  
Yamir Moreno

AbstractHypergraphs naturally represent higher-order interactions, which persistently appear in social interactions, neural networks, and other natural systems. Although their importance is well recognized, a theoretical framework to describe general dynamical processes on hypergraphs is not available yet. In this paper, we derive expressions for the stability of dynamical systems defined on an arbitrary hypergraph. The framework allows us to reveal that, near the fixed point, the relevant structure is a weighted graph-projection of the hypergraph and that it is possible to identify the role of each structural order for a given process. We analytically solve two dynamics of general interest, namely, social contagion and diffusion processes, and show that the stability conditions can be decoupled in structural and dynamical components. Our results show that in social contagion process, only pairwise interactions play a role in the stability of the absorbing state, while for the diffusion dynamics, the order of the interactions plays a differential role. Our work provides a general framework for further exploration of dynamical processes on hypergraphs.


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