The D_8-tower of weak Jacobi forms and applications

**differential**

**equations**. Expand abstract.

**differential**

**equations**. We found also a general modular

**differential**

**equation**of the generator of weight 0 and index 1 which generates the automorphic discriminant of the moduli space of Enriques surfaces.

5/10 relevant

arXiv

Computing period intergals of rigid double octic Calabi-Yau threefolds with Picard-Fuchs operator

**equations**and computations in MAPLE with a library for

**differential**

**equation**s. Expand abstract.

**equations**and computations in MAPLE with a library for

**differential**

**equations**. As a surprising consequence we also get approximations of additional integrals related to a singular (nodal) model of considered Calabi-Yau threefold.

4/10 relevant

arXiv

Convergence of the rescaled Whittaker stochastic **differential** **equations**
by independent sums

**equation**holds. The point of view in this paper is a probabilistic representation of the SDEs by independent sums. With this connection, normal and Poisson approximations fully explain the convergence. The proof extends these approximations to some particular integrated forms.

7/10 relevant

arXiv

Bridging the Gap Between Complexity Science and Clinical Practice by Formalizing Idiographic Theories: A Computational Model of Functional Analysis

**differential**

**equations**and simulated different scenarios; first, we simulated data without intervening in the system to examine the effects of avoidant coping on the development of panic symptomatic. Expand abstract.

**differential**equations, drawing on the example of a functional analysis for a patient suffering from panic disorder. We specified the system using a series of non-linear

**differential**

**equations**and simulated different scenarios; first, we simulated data without intervening in the system to examine the effects of avoidant coping on the development of panic symptomatic. Second, we formalized two clinical interventions commonly used in cognitive behavioral therapy (CBT; exposure and cognitive reappraisal) and simulated their effects on the system. The first simulation indicated that for our example patient, persistent avoidance behavior leads to an increase in catastrophic interpretations of panic-related stimuli, followed by panic symptomatic. The second simulation study illustrated

**differential**effects of the formalized CBT interventions for this patient. All tested interventions (exposure, cognitive reappraisal and combination) could decrease panic levels in the system. Formalizing clinical theories is promising in bridging the gap between complexity science and clinical practice, and can help fostering more rigorous scientific practices in psychotherapy. More precise case conceptualizations can subsequently improve intervention planning and treatment outcomes. We discuss applications in psychotherapy and future directions, amongst others concrete ways to combat technical barriers and extending the framework to incorporate interactions between individual systems, relevant for modeling social learning processes. With this report, we hope to stimulate future efforts in formalizing clinical frameworks.

5/10 relevant

PsyArXiv

Three-dimensional magnetohydrodynamics system forced by space-time white noise

**differential**

**equations**such as the Boussinesq system. Expand abstract.

**differential**

**equations**such as the Boussinesq system. Our proof is also inspired by the work of \cite{ZZ15}. To the best of the author's knowledge, this is the first result of a well-posedness of a non-linearly coupled system of

**equations**forced by a space-time white noise.

4/10 relevant

arXiv

Splitting Methods For Solving Multi-Component Transport Model: A Multicomponent Mixture for Hydrogen Plasma

**differential**

**equations**are delicate to solve and we propose to use noniterative and iterative splitting methods. Expand abstract.

**equation**with an approximation of the collision terms in the mass, momentum and energy

**equations**. The model-

**equations**are nonlinear partial

**differential**

**equations**and they are known as Stefan-Maxwell

**equations**. However, these partial

**differential**

**equations**are delicate to solve and we propose to use noniterative and iterative splitting methods. In the numerical experiments, we see the benefit of the iterative splitting methods, while these methods can relax the nonlinear terms.

4/10 relevant

arXiv

Averaging principle for slow-fast stochastic partial **differential**
**equations** with H\"{o}lder continuous coefficients

**differential**

**equations**with H\"{o}lder continuous coefficients. Expand abstract.

**differential**

**equations**with H\"{o}lder continuous coefficients. An example is also provided to explain our result.

10/10 relevant

arXiv

An Analysis of the Milstein Scheme for SPDEs without a Commutative Noise Condition

**differential**

**equations**(SPDEs) that do not possess commutative noise, one has to simulate the involved iterated stochastic integrals. Expand abstract.

**differential**

**equations**(SPDEs) that do not possess commutative noise, one has to simulate the involved iterated stochastic integrals. Recently, two approximation methods for iterated stochastic integrals in infinite dimensions were introduced in C. Leonhard and A. R\"o{\ss}ler: Iterated stochastic integrals in infinite dimensions: approximation and error estimates, Stoch. Partial Differ. Equ. Anal. Comput., 7(2): 209-239 (2019). As a result of this, it is now possible to apply the Milstein scheme by Jentzen and R\"ockner: A Milstein scheme for SPDEs, Found. Comput. Math., 15(2): 313-362 (2015) to

**equations**that need not fulfill the commutativity condition. We prove that the order of convergence of the Milstein scheme can be maintained when combined with one of the two approximation methods for iterated stochastic integrals. However, we also have to consider the computational cost and the corresponding effective order of convergence for a meaningful comparison with other schemes. An analysis of the computational cost shows that, in dependence on the equation, a combination of the Milstein scheme with both of the two methods may be the preferred choice. Further, the Milstein scheme is compared to the exponential Euler scheme and we show for different SPDEs depending on the parameters describing, e.g., the regularity of the equation, which one of the schemes achieves the highest effective order of convergence.

4/10 relevant

arXiv

Non-Existence of Finite Order Solution of Non-homogeneous Second Order
Linear **Differential** **Equations**

**differential**

**equations**. Expand abstract.

**differential**

**equations**having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of

**differential**

**equations**.

10/10 relevant

arXiv

A Phase Model with Large Time Delayed Coupling

**differential**

**equations**. Expand abstract.

**differential**

**equations**then use the weakly coupled oscillator theory to reduce it to a phase model. We assume the time delay is large, so the resulting phase model has an explicit delay in explicit delay in the argument of the phases and phase shift in the argument of the connection function. Using the phase model, we prove that for any type of oscillators and any coupling, the in-phase and anti-phase phase-locked solutions always exist and give conditions for their stability. We show that for small delay these solutions are unique, but with large enough delay multiple solutions of each type with different frequencies may occur. We give conditions for the existence and stability of other types of phase-locked solutions. We discuss the various bifurcations that can occur in the phase model as the time delay is varied. The results of the phase model analysis are applied to Morris-Lecar oscillators with diffusive coupling and compared with numerical studies of the full system of delay

**differential**

**equations**. We also consider a small time delay and compare the results with the existing ones in the literature.

5/10 relevant

arXiv