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In this paper, we present necessary conditions for the existence of weak solution of the parabolic-type equations and systems on the Heisenberg group. The main technique for proving the results relies on the method of test functions. |
This paper analyzes Bernardo Vittone’s self-invented room height method by translating it algebraically and comparing it with the arithmetic, geometric and harmonic means. The conclusion suggests that Vittone might have used the golden ratio to develop his room height method. |
We consider the stability analysis of a two-dimensional model for post-burn contraction. The model is based on morphoelasticity for permanent deformations and combined with a chemical-biological model that incorporates cellular densities, collagen density, and the concentration of chemoattractants. We formulate stability conditions depending on the decay rate of signaling molecules for both the continuous partial differential equations-based problem and the (semi-)discrete representation. We analyze the difference and convergence between the resulting spatial eigenvalues from the continuous and semi-discrete problems. |
In order to stop Value-Added Tax (VAT) fraud, EU member states use the so-called reverse-charge (RC) mechanism, which effectively removes VAT withholding and refunding in business-to-business transactions. Using the German VAT return data, we examine the effects of the introduction of RC and find that requests of input tax refunding decline sharply in the affected industries, supporting the presence of fraud prior to the introduction of RC. Based on our estimates, we quantify the revenue losses from VAT fraud prior to RC implementation in these industries to be around 5% of VAT revenues. |
The paradox of the plankton highlights the apparent contradiction between Gause’s law of competitive exclusion and the observed diversity of phytoplankton. It is well known that phytoplankton dynamics depend heavily on light availability. Here we treat light as a continuum of resources rather than a single resource by considering the visible light spectrum. We propose a spatially explicit reaction–diffusion–advection model to explore under what circumstance coexistence is possible from mathematical and biological perspectives. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and overall turbidity of the water. |
In this paper, we provide a new and more general filtration to the family of noncommutative rings known as skew PBW extensions. We introduce the notion of σ-filtered skew PBW extension and study some homological properties of these algebras. We show that the homogenization of a σ-filtered skew PBW extension A over a ring R is a graded skew PBW extension over the homogenization of R. Using this fact, we prove that if the homogenization of R is Auslander-regular, then the homogenization of A is a domain Noetherian, Artin–Schelter regular, and A is Noetherian, Zariski and (ungraded) skew Calabi–Yau. |
Innovation management is becoming more and more important for companies and especially the early stage of the innovation process, which has some problems due the volatile environment. The following design research contribution tries to take up these problems and to solve them with the situational theoretical approach. For this purpose, a new method, which is based on design thinking, was systematically and scientifically constructed through the playful aspect of gamification. In a single case study from the automotive industry, the new method could be applied in the field through three different runs and evaluated with the participants. |
In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class BSm1,1
, when both arguments belong to Triebel-Lizorkin spaces of the type Fn/pp,q(Rn). The inequalities are obtained as a consequence of a refinement of the classical Sobolev embedding Fn/pp,q(Rn)↪bmo(Rn), where we replace bmo(Rn) by an appropriate subspace which contains L∞(Rn). As an application, we study the product of functions on Fn/pp,q(Rn) when 1 |
We investigate a nonlinear equation with quadratic nonlinearities, including a nonlinear model in Silva and Freire (J. Differ. Equ. 320:371–398, 2022). Using the classical energy estimate methods, we give a necessary and sufficient condition of blow-up of solutions to nonlinear equations. We answer a problem pointed out by Silva and Freire (J. Differ. Equ. 320:371–398, 2022). |
The world has become more complicated with the introduction and development of new technologies and methods, and novel risks such as Covid-19 pandemic. Competition has been tougher than it used to be. Organizations strive to keep up with the changes in the internal and external environment. In the light of unprecedented changes, project managers must be prepared in response to the demands from their organizations and key stakeholders like clients, customers and government agencies. This book covers the fundamentals of project management, and aims to guide undergraduate and graduate students to acquire the building blocks of project management. This book also includes Microsoft Project tutorials for project scope, schedule, resources, and cost, and monitoring and controlling. |
