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We introduce a new notion of pathwise strategies for stochastic differential games. This allows us to give a correct meaning to some statement asserted in Cardaliaguet and Rainer (Appl. Math. Optim. 59: 1-36, 2009)
This paper is concerned with stochastic differential games (SDGs) defined through fully coupled forward-backward stochastic differential equations (FBSDEs) which are governed by Brownian motion and Poisson random measure. The upper and the lower value functions are defined by the doubly controlled fully coupled FBSDEs with jumps. Using a new transformation introduced in Buchdahn (Stocha Process Appl 121:2715–2750, 2011), we prove that the upper and the lower value functions are deterministic. Then, after establishing the dynamic programming principle for the upper and the lower value functions of this SDGs, we prove that the upper and the lower value functions are the viscosity solutions to the associated upper and the lower second order integral-partial differential equations of Isaacs’ type combined with an algebraic equation, respectively. Furthermore, for a special case (when σ and h do not depend on (y,z,k)), under the Isaacs’ condition, we get the existence of the value of the game.
In this study, we consider the nonlinear evolution equation of parabolic type u{sub t}−div(|∇u|{sup p−2}∇u)+f(u)=g. We analyze the long time dynamics (in the sense of global attractors) under very general conditions on the nonlinearity f. Since we do not assume any polynomial growth condition on it, the main difficulty arises at first in the proof of well-posedness. In fact, the very first contribution to this problem is a pioneering paper (Efendiev and Ôtano, Differ Int Equ 20:1201–1209, 2007) where the well-posedness result has been shown by exploiting the technique from the theory of maximal monotone operators. However, from some physical aspects, to obtain the solution in variational sense might be demanding which requires limiting procedure on the approximate solutions. In this work, we are interested in variational (weak) solution. The critical issue in the proof of well-posedness is to deal with the limiting procedure on f which is overcome utilizing the weak convergence tecniques in Orlicz spaces (Geredeli and Khanmamedov, Commun Pure Appl Anal 12:735–754, 2013; Krasnosel’skiĭ and Rutickiĭ, Convex functions and Orlicz spaces, 1961). Then, proving the existence of the global attractors in L{sup 2}(Ω) and in more regular space W{sub 0}{sup 1,p}(Ω), we show that they coincide. In addition, if f is monotone and g=0, we give an explicit estimate of the decay rate to zero of the solution.
We study a dynamical thin shallow shell whose elastic deformations are described by a nonlinear system of Marguerre–Vlasov’s type under the presence of thermal effects. Our main result is the proof of a global existence and uniqueness of a weak solution in the case of clamped boundary conditions. Standard techniques for uniqueness do not work directly in this case. We overcame this difficulty using recent work due to Lasiecka (Appl Anal 4:1376–1422, 1998).
In this paper we study the optimal control problem for a class of general mean-field stochastic differential equations, in which the coefficients depend, nonlinearly, on both the state process as well as of its law. In particular, we assume that the control set is a general open set that is not necessary convex, and the coefficients are only continuous on the control variable without any further regularity or convexity. We validate the approach of Peng (SIAM J Control Optim 2(4):966–979, 1990) by considering the second order variational equations and the corresponding second order adjoint process in this setting, and we extend the Stochastic Maximum Principle of Buckdahn et al. (Appl Math Optim 64(2):197–216, 2011) to this general case.
Online mapping services from Google, Apple, and Microsoft are exceedingly popular applications for exploring 3D urban cities. Their explosive growth provides impetus for photorealistic 3D modeling of urban scenes. Although classical algorithms such as multiview stereo and laser range scanners are traditional sources for detailed 3D models of existing structures, they generate heavyweight models that are not appropriate for the streaming data that these navigation applications leverage. Instead, lightweight models as produced by interactive image-based tools are better suited for this domain. The contribution of this work is that it merges the benefits of multiview geometry, an intuitive sketching interface, and dynamic texture mapping to produce lightweight photorealistic 3D models of buildings. We present experimental results from urban scenes using our PhotoSketch system.
Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25–51, 2015; Lyttle et al. in Biol Cybern 111(1):25–47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701–744, 2021. https://doi.org/10.1137/20M1344974) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates’ hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.
Instrument downtime leads to uncertainty in the monthly and annual record of cloud fraction (CF), making it difficult to perform time series analyses of cloud properties and perform detailed evaluations of model simulations. As cloud occurrence is partially controlled by the large-scale atmospheric environment, this knowledge is used to reduce uncertainties in the instrument record. Synoptic patterns diagnosed from the North American Regional Reanalysis (NARR) during the period 1997–2010 are classified using a competitive neural network known as the self-organizing map (SOM). The classified synoptic states are then compared to the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) instrument record to determine the expected CF. A number of SOMs are tested to understand how the number of classes and the period of classifications impact the relationship between classified states and CFs. Bootstrapping is utilized to quantify the uncertainty of the instrument record when statistical information from the SOM is included. Although all SOMs significantly reduce the uncertainty of the CF record calculated in Kennedy et al. (Theor Appl Climatol 115:91–105, 2014), SOMs with a large number of classes and separated by month are required to produce the lowest uncertainty and best agreement with the annual cycle of CF. Lastly, this result may be due to a manifestation of seasonally dependent biases in NARR.
Electroplated bismuth (Bi) is commonly used in transition-edge sensors (TESs) for X-rays because of its high stopping power and low heat capacity (Collan in Phys Rev B 1:2888, 1970, Yan in Appl Phys Lett 111:192602, 2017). Electroplated Bi is usually grown on top of another metal that acts as seed layer, typically gold (Au), making it challenging to extrapolate its thermoelectric properties. In this work, we present four-wire resistance measurement structures that allow us to measure resistance as a function of temperature of electroplated Bi independently of Au. The results show that the thermal conductivity of the Bi at 3 K is high enough to ensure the correct thermalization of X-ray photons when used as an absorber for TESs.
Vast amounts of co-streams are generated from plant and animal-based food processing industries. Efficient utilization of these co-streams is important from an economic and environmental perspective. Non-utilization or under-utilization of co-streams results in loss of potential revenues, increased disposal cost of these products and environmental pollution. At present, extensive research is taking place around the globe towards recycling of co-streams to generate value-added products. This review evaluates various co-streams from food processing industries as raw materials in developing biodegradable agricultural mulching applications. Among the agriculture-based co-streams, potato peels, tomato peels, carrot residues, apple pomace, coffee residues and peanut residues were reviewed with respect to production amount, composition, film forming components and film forming capabilities. Similarly, selected co-streams from slaughterhouses, poultry and fish processing industries were also reviewed and evaluated for the same purpose.
We define certain criteria, using the characteristic decomposition of the boundary conditions and energy estimates, which a set of stable boundary conditions for a linear initial boundary value problem, involving a symmetric hyperbolic system, must satisfy. We first use these stability criteria to show the instability of the Maxwell boundary conditions proposed by Grad (Commun Pure Appl Math 2(4):331–407, 1949). We then recognise a special block structure of the moment equations which arises due to the recursion relations and the orthogonality of the Hermite polynomials; the block structure will help us in formulating stable boundary conditions for an arbitrary order Hermite discretization of the Boltzmann equation. The formulation of stable boundary conditions relies upon an Onsager matrix which will be constructed such that the newly proposed boundary conditions stay close to the Maxwell boundary conditions at least in the lower order moments.
In this paper we study first-passage percolation in the configuration model with empirical degree distribution that follows a power-law with exponent τ∈(2,3). We assign independent and identically distributed (i.i.d.) weights to the edges of the graph. We investigate the weighted distance (the length of the shortest weighted path) between two uniformly chosen vertices, called typical distances. When the underlying age-dependent branching process approximating the local neighborhoods of vertices is found to produce infinitely many individuals in finite time—called explosive branching process—Baroni, Hofstad and the second author showed in Baroni et al. (J Appl Probab 54(1):146–164, 2017) that typical distances converge in distribution to a bounded random variable. The order of magnitude of typical distances remained open for the τ∈(2,3) case when the underlying branching process is not explosive. We close this gap by determining the first order of magnitude of typical distances in this regime for arbitrary, not necessary continuous edge-weight distributions that produce a non-explosive age-dependent branching process with infinite mean power-law offspring distributions. This sequence tends to infinity with the amount of vertices, and, by choosing an appropriate weight distribution, can be tuned to be any growing function that is O(loglog n), where n is the number of vertices in the graph. We show that the result remains valid for the the erased configuration model as well, where we delete loops and any second and further edges between two vertices.
Quasi-chemical model, which is widely used for nucleation description, is revised on the basis of recent results in studying of non-equilibrium effects in reacting gas mixtures (Kolesnichenko and Gorbachev in Appl Math Model 34:3778–3790, 2010; Shock Waves 23:635–648, 2013; Shock Waves 27:333–374, 2017). Non-equilibrium effects in chemical reactions are caused by the chemical reactions themselves and therefore these contributions should be taken into account in the corresponding expressions for reaction rates. Corrections to quasi-equilibrium reaction rates are of two types: (a) spatially homogeneous (caused by physical–chemical processes) and (b) spatially inhomogeneous (caused by gas expansion/compression processes and proportional to the velocity divergency). Both of these processes play an important role during the nucleation and are included into the proposed model. The method developed for solving the generalized Boltzmann equation for chemically reactive gases is applied for solving the set of equations of the revised quasi-chemical model. It is shown that non-equilibrium processes lead to essential deviation of the quasi-stationary distribution and therefore the nucleation rate from its traditional form.
We consider the sequence of Gibbs measures of Ising models with Kac interaction defined on a periodic two-dimensional discrete torus near criticality. Using the convergence of the Glauber dynamic proven by Mourrat and Weber (Commun Pure Appl Math 70:717–812, 2017) and a method by Tsatsoulis and Weber employed in ( arXiv:1609.08447 2016), we show tightness for the sequence of Gibbs measures of the Ising–Kac model near criticality and characterise the law of the limit as the Φ{sub 2}{sup 4} measure on the torus. Our result is very similar to the one obtained by Cassandro et al. (J Stat Phys 78(3):1131–1138, 1995) on ℤ{sup 2}, but our strategy takes advantage of the dynamic, instead of correlation inequalities. In particular, our result covers the whole critical regime and does not require the large temperature/large mass/small coupling assumption present in earlier results.
We study the quantitative pointwise behavior of the solutions of the linearized Boltzmann equation for hard potentials, Maxwellian molecules and soft potentials, with Grad’s angular cutoff assumption. More precisely, for solutions inside the finite Mach number region (time like region), we obtain the pointwise fluid structure for hard potentials and Maxwellian molecules, and optimal time decay in the fluid part and sub-exponential time decay in the non-fluid part for soft potentials. For solutions outside the finite Mach number region (space like region), we obtain sub-exponential decay in the space variable. The singular wave estimate, regularization estimate and refined weighted energy estimate play important roles in this paper. Our results extend the classical results of Liu and Yu (Commun Pure Appl Math 57:1543–1608, 2004), (Bull Inst Math Acad Sin 1:1–78, 2006), (Bull Inst Math Acad Sin 6:151–243, 2011) and Lee et al. (Commun Math Phys 269:17–37, 2007) to hard and soft potentials by imposing suitable exponential velocity weight on the initial condition.
In a previous paper (Funct. Anal. Appl., 3 (2015), 205–209), we defined quantum Markov states. Here we recall this definition and present a proof of the results from that paper (which are given there without proofs). We give a definition of a quantum hidden Markov state generated by a function of a quantum Markov process and show how it is related to other definitions of such states. Our definitions work for quantum Markov fields on ℤ{sup N} and on graphs. We consider an example with the Cayley tree.
Mixed ionic-electronic conducting (MIEC) membranes have a great potential for use in gas separation technology in the production of pure oxygen for metallurgy, micro- and nanoelectronics, biotechnology, pharmaceutics, etc. Before this happens, an important issue has to be addressed. This issue involves the design of novel MIEC membranes with enhanced oxygen transport. Recently, a concept of thick two-layer solid/liquid composite MIEC-Redox membranes with accelerated diffusion-bubbling oxygen transfer was proposed (see Belousov and Fedorov in ACS Appl Mater Interfaces 10:21794–21798, 2018). These diffusion-bubbling membranes could serve for efficient oxygen separation from air. However, there is no enough fundamental understanding of the mass transport processes involved. This understanding is important for evaluating the potential of MIEC-Redox membranes for practical application. The presented article gives a theory of oxygen mass transfer in two-layer copper and vanadium oxide-based MIEC-Redox membranes. The theory describes both the transport of oxygen ions in the outer layer of the membrane and the nucleation, growth, and transport of oxygen gas bubbles in the inner layer of the membrane. Kinetic regularities of oxygen mass transfer are established. The ways to enhance the productivity of MIEC-Redox membranes are outlined.
Under direct laser desorption/ionization mass spectrometric conditions, the irradiation of target spots made of gold nanoparticle residues generates a series of peaks at m/z 197, 394, 591… representing Au{sub n}{sup −} ions (n = 1–3). In contrast, spectra recorded from gold nanoparticles directly mixed with an alkali cyanide exhibited an additional peak at m/z 249, indicating an abundant generation of gaseous [Au(CN){sub 2}]{sup −} ions upon irradiation. The relative intensity of the m/z 249 peak surged when the amount of cyanide in the mixture was increased. Most remarkably, a peak at m/z 249 was observed even from neat AuNPs upon irradiation, if a nearby spot, which was not irradiated, happened to bear a cyanide sample. We postulated that traces of HCN emanating from the headspace of aqueous cyanide solution during the sample-plate preparation is sufficient to convert gold to AuCN, which is subsequently detected as [Au(CN){sub 2}]{sup −}. Further experiments demonstrated that the relative intensity of the m/z 249 peak diminishes exponentially as the AuNP spot becomes more distant from the putative HCN source. Eventually, the method was developed as an efficient procedure to detect HCN or alkali cyanides. Using KCN, the detection limits were determined to be below 10 pg of CN{sup −} per spot. The method also demonstrated that, upon crushing, the seeds or roots of certain fruits and vegetables such as apple, peach, radish, and cassava, but not carrot, release HCN in amounts detectable by this method. .