Spectrally isometric elementary operators

We present criteria for unital elementary operators (of small length) on unital semisimple Banach algebras to be spectral isometries. The surjective ones among them turn out to be algebra automorphisms.

More elementary operators that are spectrally bounded

We discuss some necessary and some sufficient conditions for an elementary operator x↦∑ⁿ_i=1a_ixb_i on a Banach algebra A to be spectrally bounded. In the case of length three, we obtain a complete characterisation when A acts irreducibly on a Banach space of dimension greater than three.

Locally quasi-nilpotent elementary operators

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σⁿ _i=1 M_ai,_bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_ia_j : 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σⁿ _i=1 M_ui,_vi with v_iu_j = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.

Elementary operators-still not elementary?

Properties of elementary operators, that is, finite sums of two-sided multiplications on a Banach algebra, have been studied under a vast variety of aspects by numerous authors. In this paper we review recent advances in a new direction that seems not to have been explored before: the question when an elementary operator is spectrally bounded or spectrally isometric. As with other investigations, a number of subtleties occur which show that elementary operators are still not elementary to handle.

Non-Gaussian distribution of collective operators in quantum spin chains

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum fluctuations at criticality lead to highly non-Gaussian distributions. Interestingly, we show that the distributions for different system sizes collapse on thesame curve after scaling for a wide range of transitions: first and second order quantum transitions and transitions of the Berezinskii–Kosterlitz–Thouless type. We propose and analyse the feasibility of an experimental reconstruction of the distribution using light–matter interfaces for atoms in optical lattices or in optical resonators.

Orbits of semigroups of truncated convolution operators

We prove that a semigroup generated by finitely many truncated convolution operators on $L_p[0, 1]$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion

Recently, Bès, Martin, and Sanders [11] provided examples of disjoint hypercyclic operators which fail to satisfy the Disjoint Hypercyclicity Criterion. However, their operators also fail to be disjoint weakly mixing. We show that every separable, infinite dimensional Banach space admits operators T1,T2,…,TN with N⩾2 which are disjoint weakly mixing, and still fail to satisfy the Disjoint Hypercyclicity Criterion, answering a question posed in [11]. Moreover, we provide examples of disjoint hypercyclic operators T1, T2 whose corresponding set of disjoint hypercyclic vectors is nowhere dense, answering another question posed in [11]. In fact, we explicitly describe their set of disjoint hypercyclic vectors. Those same disjoint hypercyclic operators fail to be disjoint topologically transitive. Lastly, we create examples of two families of d-hypercyclic operators which fail to have any d-hypercyclic vectors in common.

Eigenfunctions and fundamental solutions of the fractional Laplace and Dirac operators: the Riemann-Liouville case

In this paper we study eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator $\Delta_+^{(\alpha,\beta,\gamma)}:= D_{x_0^+}^{1+\alpha} +D_{y_0^+}^{1+\beta} +D_{z_0^+}^{1+\gamma},$ where $(\alpha, \beta, \gamma) \in \,]0,1]^3$, and the fractional derivatives $D_{x_0^+}^{1+\alpha}$, $D_{y_0^+}^{1+\beta}$, $D_{z_0^+}^{1+\gamma}$ are in the Riemann-Liouville sense. Applying operational techniques via two-dimensional Laplace transform we describe a complete family of eigenfunctions and fundamental solutions of the operator $\Delta_+^{(\alpha,\beta,\gamma)}$ in classes of functions admitting a summable fractional derivative. Making use of the Mittag-Leffler function, a symbolic operational form of the solutions is presented. From the obtained family of fundamental solutions we deduce a family of fundamental solutions of the fractional Dirac operator, which factorizes the fractional Laplace operator. We apply also the method of separation of variables to obtain eigenfunctions and fundamental solutions.

Coordination in humanitarian logistics through clusters

Purpose – In the field of humanitarianism, cluster thinking has been suggested as a solution to the lack of coordinated disaster response. Clusters for diverse functions, including sheltering, logistics and water and sanitation, can be viewed as an effort to achieve functional coordination. The purpose of this paper is to contribute to a greater understanding of the potential of cluster concepts using supply chain coordination and inter‐cluster coordination. The focus is on the conceptual level rather than on specific means of coordination. Design/methodology/approach – The cluster concept in humanitarian relief, along with some key empirical issues, is based on a case study. The concept is then compared to the literature on clusters and coordination in order to develop a theoretical framework with propositions on the tradeoffs between different types of coordination. Findings – The results provide important reflections on one of the major trends in contemporary development of humanitarian logistics. This paper shows that there is a tradeoff between different types of coordination, with horizontal coordination inside cluster drawing attention away from important issues of the supply chain as well as the need to coordinate among the clusters. Research limitations/implications – There is a need for more in‐depth case studies of experiences with clusters in various operations. Various perspectives should be taken into account, including the field, responding agencies, beneficiaries, donors, military and commercial service providers, both during and between disasters. Practical implications – The paper presents the tradeoffs between different types of coordination, in which basic aims such as standardisation through functional coordination, must be balanced with cross‐functional and vertical coordination in order to more successfully serve the users' composite needs. Originality/value – The focus on possible trade‐offs between different types of coordination is an important complement to the literature, which often assumes simultaneous high degrees of horizontal and vertical coordination.

Theory development in humanitarian logistics : A framework and three cases

Purpose: There is a need for theory development within the field of humanitarian logistics to understand logistics needs in different stages of a crisis and how to meet these. This paper aims to discuss three dimensions identified in logistics and organization theories and how they relate to three different cases of humanitarian logistics operations - the regional concept of the International Federation of Red Cross Red Crescent Societies, the development and working of the United Nations Joint Logistics Centre and coordination challenges of military logistics in UN mandated peacekeeping operations. The purpose is to build a framework to be used in further studies. Design/methodology/approach: A framework for the study of humanitarian logistics along three dimensions is developed, followed by a discussion of the chosen cases in relation to these dimensions. The framework will be used as basis for the case studies to be undertaken for the purpose of understanding and identification of new questions and needs for other or revised concepts from theory. Findings: The paper shows the relevance of a wide literature to the issues pertinent to humanitarian logistics. There is considerable promise in extant literature on logistics, SCM and coordination, but this needs to be confronted with the particular issues seen in the humanitarian logistics setting to achieve further theory development. Originality/value: The major contribution of the paper lies in its breadth of theoretical perspectives presented and combined in a preliminary theoretical framework. This is applied more specifically in the three case studies described in the paper.

Pico Cell Integration to Operator’s Incident Management Process

Mobile network coverage is traditionally provided by outdoor macro base stations, which have a long range and serve several of customers. Due to modern passive houses and tightening construction legislation, mobile network service is deteriorated in many indoor locations. Typically, solutions for indoor coverage problem are expensive and demand actions from the mobile operator. Due to these, superior solutions are constantly researched. The solution presented in this thesis is based on Small Cell technology. Small Cells are low power access nodes designed to provide voice and data services.. This thesis concentrates on a specific Small Cell solution, which is called a Pico Cell. The problem regarding Pico Cells and Small Cells in general is that they are a new technological solution for the mobile operator, and the possible problem sources and incidents are not properly mapped. The purpose of this thesis is to figure out the possible problems in the Pico Cell deployment and how they could be solved within the operator’s incident management process. The research in the thesis is carried out with a literature research and a case study. The possible problems are investigated through lab testing. Pico Cell automated deployment process was tested in the lab environment and its proper functionality is confirmed. The related network elements were also tested and examined, and the emerged problems are resolvable. Operators existing incident management process can be used for Pico Cell troubleshooting with minor updates. Certain pre-requirements have to be met before Pico Cell deployment can be considered. The main contribution of this thesis is the Pico Cell integrated incident management process. The presented solution works in theory and solves the problems found during the lab testing. The limitations in the customer service level were solved by adding the necessary tools and by designing a working question pattern. Process structures for automated network discovery and pico specific radio parameter planning were also added for the mobile network management layer..

Designing gainsharing model variations with logistics service company

This thesis studies, in collaboration with a Finnish logistics service company, gainsharing and the development of a gainsharing models in a logistics outsourcing context. The purpose of the study is to create various gainsharing model variations for the use of a service provider and its customers in order to develop and enhance the customer’s processes and operations, create savings and improve the collaboration between the companies. The study concentrates on offering gainsharing model alternatives for companies operating in internal logistics outsourcing context. Additionally, the prerequisites for the gainsharing arrangement are introduced. In the beginning of the study an extensive literature review is conducted. There are three main themes explored which are the collaboration in an outsourcing context, key account management and gainsharing philosophy. The customer expectations and experiences are gathered by interviewing case company’s employees and its key customers. In order to design the gainsharing model prototypes, customers and other experts’ knowledge and experiences are utilized. The result of this thesis is five gainsharing model variations that are based on the empirical and theoretical data. In addition, the instructions related to each created model are given to the case company, but are not available in this paper

Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Generation of a business plan for a logistics service provider

The purpose of this Master’s Thesis was to study the suitability of transportation of liquid wastes to the portfolio of the case company. After the preliminary study the waste types were narrowed down to waste oil and oily waste from ports. The thesis was executed by generating a business plan. The qualitative research of this Master’s Thesis was executed as a case study by collecting information from multiple sources. The business plan was carried out by first familiarizing oneself with literature related to business planning which was then used as a base for the interview of the customer and interviews of the personnel of the case company. Additionally, internet sources and informal conversational interviews with the personnel of the case company were used and these interviews took place during the preliminary study and this thesis. The results of this thesis describe the requirements for the case company that must be met to be able to start operations. Import of waste oil fits perfectly to the portfolio of the case company and it doesn’t require any big investments. Success of the import of waste oil is affected by price of crude oil, exchange rate of ruble and legislation among others. Transportation of oily waste from ports, in turn, is not a core competence of the case company so more actions are required to start operating such as subcontracting with a waste management company.