A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

Stability and related properties of vacua and ground states

We consider the formal non-relativistic limit (nrl) of the : phi(4):(s+1) relativistic quantum field theory (rqft), where s is the space dimension. Following the work of R. Jackiw [R. Jackiw, in: A. Ali, P. Hood-bhoy (Eds.), Beg Memorial Volume, World Scientific, Singapore, 1991], we show that, for s = 2 and a given value of the ultraviolet cutoff K, there are two ways to perform the nrl: (i) fixing the renormalized mass m(2) equal to the bare mass m(0)(2); (ii) keeping the renormalized mass fixed and different from the bare mass mo. In the (infinite-volume) two-particle sector the scattering amplitude tends to zero as K -> infinity in case (i) and, in case (ii), there is a bound state, indicating that the interaction potential is attractive. As a consequence, stability of matter fails for our boson system. We discuss why both alternatives do not reproduce the low-energy behaviour of the full rqft. The singular nature of the nrl is also nicely illustrated for s = 1 by a rigorous stability/instability result of a different nature. (C) 2007 Elsevier Inc. All rights reserved.

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.

Electronic Structure of the Ground and Low-Lying Electronic States of MoB and MoB(+)

Multiconfigurational second-order perturbation theory (CASSCF//CASPT2) and quadruple-zeta ANO-RCC basis sets were employed to investigate the ground and low-lying electronic states of MoB and MoB(+). Spectroscopic constants, potential energy curves, wavefunctions, Mulliken population analyses, and ionization energies are given. The ground state of MoB is of X(6)Pi symmetry (R(e) = 1.968 angstrom, omega(e) = 664 cm(-1), and mu = 2.7 D), giving rise to a Omega = 7/2 ground state after including spin-orbit coupling. For MoB(+), the ground state is computed to be of X(7)Sigma(+) symmetry (R(e) = 2.224 angstrom, omega(e) = 141 cm(-1), and mu = 1.2 D), with an adiabatic ionization energy of 7.19 eV and a vertical one of 7.53 eV. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3362-3370, 2011

Electronic structure and chemical bonding in the ground states of Tc(2) and Re(2)

Multiconfiguration second-order perturbation theory, including relativistic effects and spin-orbit coupling, has been employed to investigate the nature of the chemical bonding in the ground state of Tc(2) and Re(2). The Tc(2) ground state is found to be a 0(g)(+) state, with an effective bond order (EBO) of 4.4, and a dissociation energy of 3.25 eV. The Re(2) ground state is a 1(g) state, with EBO = 4.3. Almost degenerate to it, is a 0(g)(+) state (T(e) = 77 cm(-1)), with EBO = 4.1. Experimental evidence also indicates that the ground state is of 1(g) nature. The dissociation energy is computed to be 5.0 eV in agreement with an experimental estimate of 4 +/- 1 eV.

Electronic Structure and Chemical Bonding in the Ground and Low-Lying Electronic States of Ta(2)

The electronic structure and chemical bonding of the ground and low-lying Lambda - S and Omega states of Ta(2) were investigated at the multiconfiguration second-order perturbation theory (CASSCF//CASPT2) level. The ground state of Ta(2) is computed to be a X(3)Sigma(-)(g) state (R(e) = 2.120 angstrom, omega(e) = 323 cm(-1), and D(e) = 4.65 eV), with two low-lying singlet states close to it (a(1) Sigma(+)(g) : T(e) = 409 cm(-1), R(e) = 2.131 angstrom, and omega(e) = 313 cm(-1); b(1) Gamma(g): T(e) = 1, 038 cm(-1), R(e) = 2.127 angstrom, and omega(e) = 316 cm(-1)). These electronic states are derived from the same electronic configuration: vertical bar 13 sigma(2)(g)14 sigma(2)(g)7 delta(2)(g)13 pi(4)(u)>. The effective bond order of the X(3) Sigma(-)(g) state is 4.52, which indicates that the Ta atoms are bound by a quintuple chemical bond. The a(1) Sigma(+)(g) state interacts strongly with the X(3)Sigma(-)(g) g ground state by a second-order spin-orbit interaction, giving rise to the (1)0(g)(+) (ground state) (dominated by the X(3)Sigma(-)(g) Lambda - S ground state) and (9)0(g)(+) (dominated by the a(1) Sigma(+)(g) Lambda - S state) Omega states. These results are in line with those reported for the group 5B homonuclear transition metal diatomics. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 1306-1315, 2011

Higher Ground : Stevie Wonder och New Age

Syftet med min uppsats är att jämföra religiösa företeelser från tre av Stevie Wonders album med New Age för att på så sätt uttröna om Stevie Wonders texter påverkats av New Age- föreställningar. Jag hittar både skillnader och likheter när jag jämför det religiösa budskapet i Stevie Wonders texter med New Age. De New Age- företeelser som går att hitta i texterna är få i förhållande till New Age i sin helhet och det är svårt att avgöra vilka influenser som kommer ifrån Stevie Wonder, New Age eller den omgivande motståndsrörelsen. Det finns dock, enligt mig, absolut en koppling.

The remote control ofmobile robot on theInternet

During last decades, the Internet teleobotics has been growing at an enormous ratedue to the rapid improvement of Internet technology. This paper presents theinternet-based remote control of mobile robot. To face unpredictable Internet delaysand possible connection rupture, a direct continuous control based teleoperationarchitecture with “Speed Limit Module” (SLM) and “Delay Approximator” (DA) isproposed. This direct continuous control architecture guarantees the path error of therobot motion is restricted within the path error tolerance of the application.Experiment results show the feasibility and effectiveness of this direct Internet controlarchitecture in the real Internet environment.

Simulation of Photovoltaic Panel Production as Complement to Ground Source Heat Pump System

This master thesis presents a new technological combination of two environmentally friendly sources of energy in order to provide DHW, and space heating. Solar energy is used for space heating, and DHW production using PV modules which supply direct current directly to electrical heating elements inside a water storage tank. On the other hand a GSHP system as another source of renewable energy provides heat in the water storage tank of the system in order to provide DHW and space heating. These two sources of renewable energy have been combined in this case-study in order to obtain a more efficient system, which will reduce the amount of electricity consumed by the GSHP system.The key aim of this study is to make simulations, and calculations of the amount ofelectrical energy that can be expected to be produced by a certain amount of PV modules that are already assembled on a house in Vantaa, southern Finland. This energy is then intended to be used as a complement to produce hot water in the heating system of the house beside the original GSHP system. Thus the amount of electrical energy purchased from the grid should be reduced and the compressor in the GSHP would need fewer starts which would reduce the heating cost of the GSHP system for space heating and providing hot water.The produced energy by the PV arrays in three different circuits will be charged directly to three electrical heating elements in the water storage tank of the existing system to satisfy the demand of the heating elements. The excess energy can be used to heat the water in the water storage tank to some extent which leads to a reduction of electricity consumption by the different components of the GSHP system.To increase the efficiency of the existing hybrid system, optimization of different PV configurations have been accomplished, and the results are compared. Optimization of the arrays in southern and western walls shows a DC power increase of 298 kWh/year compared with the existing PV configurations. Comparing the results from the optimization of the arrays on the western roof if the intention is to feed AC power to the components of the GSHP system shows a yearly AC power production of 1,646 kWh.This is with the consideration of no overproduction by the PV modules during the summer months. This means the optimized PV systems will be able to cover a larger part of summer demand compared with the existing system.

Game Audio in Audio Games : Towards a Theory on the Roles and Functions of Sound in Audio Games

For the past few decades, researchers have increased our understanding of how sound functions within various audio–visual media formats. With a different focus in mind, this study aims to identify the roles and functions of sound in relation to the game form Audio Games, in order to explore the potential of sound when acting as an autonomous narrative form. Because this is still a relatively unexplored research field, the main purpose of this study is to help establish a theoretical ground and stimulate further research within the field of audio games. By adopting an interdisciplinary approach to the topic, this research relies on theoretical studies, examinations of audio games and contact with the audio game community. In order to reveal the roles of sound, the gathered data is analyzed according to both a contextual and a functional perspective. The research shows that a distinction between the terms ‘function’ and ‘role’ is important when analyzing sound in digital games. The analysis therefore results in the identification of two analytical levels that help define the functions and roles of an entity within a social context, named the Functional and the Interfunctional levels. In addition to successfully identifying three main roles of sound within audio games—each describing the relationship between sound and the entities game system, player and virtual environment—many other issues are also addressed. Consequently, and in accordance with its purpose, this study provides a broad foundation for further research of sound in both audio games and video games.

Thomas-Fermi ground state of dipolar fermions in a circular storage ring

Recent developments in the field of ultracold gases has led to the production of degenerate samples of polar molecules. These have large static electric-dipole moments, which in turn causes the molecules to interact strongly. We investigate the interaction of polar particles in waveguide geometries subject to an applied polarizing field. For circular waveguides, tilting the direction of the polarizing field creates a periodic inhomogeneity of the interparticle interaction. We explore the consequences of geometry and interaction for stability of the ground state within the Thomas-Fermi model. Certain combinations of tilt angles and interaction strengths are found to preclude the existence of a stable Thomas-Fermi ground state. The system is shown to exhibit different behavior for quasi-one-dimensional and three-dimensional trapping geometries.