A cross-sector international study of remote work and its management in the pandemic

With the Covid-19 pandemic forcing organizations to work remotely, this paper presents a wide-ranging study of factors affecting the transition from physical to online operations, and the management and conduct of business online. A literature review summarizes years of research on remote work, while an international survey done in August 2020 collects input from managers in 158 organizations dealing with pandemic-related lockdowns. Topics include impacts on productivity, employee morale, and management workload. Sampled organizations range from manufacturing and retail firms to schools and universities. Cross-sector analysis allows inquiry into why, for instance, productivity and morale may decline in some places but improve in others

Time-Changed Poisson Processes

We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDE's. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDE's corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index $0<\beta<1,$ when $\beta$ is a rational number. We then use this result to obtain the governing DDE for the mass function of Poisson process time-changed by tempered stable subordinator. Our results extend and complement the results in Baeumer et al. \cite{B-M-N} and Beghin et al. \cite{BO-1} in several directions.Comment: 18 page

Maximal LpL^p-regularity for stochastic evolution equations

We prove maximal $L^p$-regularity for the stochastic evolution equation \{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}. under the assumption that $A$ is a sectorial operator with a bounded $H^\infty$-calculus of angle less than $\frac12\pi$ on a space $L^q(\mathcal{O},\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\in (2,\infty)$ and $q\in [2,\infty)$ and initial conditions $u_0$ in the real interpolation space \XAp we prove existence of unique strong solution with trajectories in L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to \g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their second variables with small enough Lipschitz constants. Extensions to the case where $A$ is an adapted operator-valued process are considered as well. Various applications to stochastic partial differential equations are worked out in detail. These include higher-order and time-dependent parabolic equations and the Navier-Stokes equation on a smooth bounded domain \OO\subseteq \R^d with $d\ge 2$. For the latter, the existence of a unique strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables, respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981).Comment: revised version, to appear in: Stoch. Process. App

The operational-reliability assessment of a power supply for the alarm system of a transport facility

The following paper presents issues concerning a power supply for the alarm systems used in transport facilities. It describes the guidelines included in the polish standard PN-EN 50131-1:2009 „Systemy alarmowe – Systemy sygnalizacji włamania i napadu – Wymagania systemowe” (Alarm systems – intrusion and hold-up systems – system requirements), a power supply in particular. Then the operational-reliability assessment of a system consisting of a main power supply (230V AC power grid), redundant UPS and diesel generator was made. The aim of that was to obtain formulas for particular state probability values in a symbolic form (Laplace’s). The further assessments taking other types of power supply into account will be presented in the forthcoming papers

Selected aspects of reliability-exploitation analysis of power supply of highway telematics systems

W artykule zaprezentowano analizę dwutorowego układu zasilania systemu telematyki autostradowej w aspekcie niezawodnościowoeksploatacyjnym. Przyjmując trzy stany (pełnej zdatności SPZ, zagrożenia bezpieczeństwa QZB i zawodności bezpieczeństwa QB) oraz określone przejścia pomiędzy nimi, wyznaczono zależności pozwalające na wyznaczenie prawdopodobieństw przebywania układu zasilania systemu telematyki autostradowej w wymienionych stanach.The reliability of functioning of highway telematics systems requires ensuring the adequate supply of the devices they consist of. Their failure is a failure in the system, which may result in interruption of the operation of the whole or a part of the system. Therefore, the devices are usually supplied from two sources. The first one is the main power supply. In the case of the main power supply failure, the system is automatically switched to the reserve power source. The paper presents the analysis of a two-way power supply of highway telematics system in terms of reliability-exploitation. Assuming three states (full ability SPZ, impendency over safety QZB and unreliability of safety QB) and certain transitions between them, there were determined the probabilities of staying the power supply highway telematics systems in those states

Role of video monitoring systems in railway transport in increasing passengers' safety

Przedstawiono problematykę analogowych i cyfrowych systemów monitoringu wizyjnego, łącznie z wykorzystaniem sieci ethernetowych. Opisano koncepcję zintegrowanego systemu monitoringu wizyjnego dla obiektów wykorzystywanych w transporcie kolejowym. Nadrzędnym celem proponowanego rozwiązania jest zwiększenie bezpieczeństwa zarówno pasażerów, jak i przewożonych towarów.The document presents the issue of analogue and digital video monitory together with the use of Ethernet networks. The article describes the conception of an integrated video monitoring system for rail transport objects. The most important purpose of the proposed solution is to increase the safety of passengers and freight