Intertwining Laplace Transformations of Linear Partial Differential Equations

We propose a generalization of Laplace transformations to the case of linear partial differential operators (LPDOs) of arbitrary order in R^n. Practically all previously proposed differential transformations of LPDOs are particular cases of this transformation (intertwining Laplace transformation, ILT). We give a complete algorithm of construction of ILT and describe the classes of operators in R^n suitable for this transformation. Keywords: Integration of linear partial differential equations, Laplace transformation, differential transformationComment: LaTeX, 25 pages v2: minor misprints correcte

Conjugation of injections by permutations

Let X be a countably infinite set, and let f, g, and h be any three injective self-maps of X, each having at least one infinite cycle. (For instance, this holds if f, g, and h are not bijections.) We show that there are permutations a and b of X such that h=afa^{-1}bgb^{-1} if and only if |X\Xf|+|X\Xg|=|X\Xh|. We also prove a version of this statement that holds for infinite sets X that are not necessarily countable. This generalizes results of Droste and Ore about permutations.Comment: 27 pages, 4 figure

On Solving a Generalized Chinese Remainder Theorem in the Presence of Remainder Errors

In estimating frequencies given that the signal waveforms are undersampled multiple times, Xia et. al. proposed to use a generalized version of Chinese remainder Theorem (CRT), where the moduli are $M_1, M_2, \cdots, M_k$ which are not necessarily pairwise coprime. If the errors of the corrupted remainders are within \tau=\sds \max_{1\le i\le k} \min_{\stackrel{1\le j\le k}{j\neq i}} \frac{\gcd(M_i,M_j)}4, their schemes can be used to construct an approximation of the solution to the generalized CRT with an error smaller than $\tau$. Accurately finding the quotients is a critical ingredient in their approach. In this paper, we shall start with a faithful historical account of the generalized CRT. We then present two treatments of the problem of solving generalized CRT with erroneous remainders. The first treatment follows the route of Wang and Xia to find the quotients, but with a simplified process. The second treatment considers a simplified model of generalized CRT and takes a different approach by working on the corrupted remainders directly. This approach also reveals some useful information about the remainders by inspecting extreme values of the erroneous remainders modulo $4\tau$. Both of our treatments produce efficient algorithms with essentially optimal performance. Finally, this paper constructs a counterexample to prove the sharpness of the error bound $\tau$

The role of maritime transport sector from the perspective of energy and gender: The case of South Pacific

This paper discusses sustainable use of energy from a feminist perspective and focuses on the role of maritime transport sector in terms of energy access for rural women as users of maritime transport. In many parts of the world, the priorities of energy use tend to be gendered. Women are often excluded from decision-making process of energy choice and access. In the South Pacific where adequate recycling facilities and markets are not easily accessible, wastes are a big concern for their environments. An emerging concept of \u27circular economy\u27 to closing the loop of product life-cycles poses a challenge but also an opportunity for many South Pacific communities. For example, some rural women entrepreneurs found a business chance in waste management to participate in circular economy. One of the biggest obstacles encountered by them was, however, an access to ships to transport collected recycling items (e.g., used batteries) to recycling facilities overseas. In this paper, we argue whether a gendered nature of maritime transport may be limiting their capacity to provide services to minority users like women and what would be the role of maritime transport sector to support women\u27s contribution to establishing a sustainable, energy efficient society. The paper concludes that a missing link between women\u27s economic participation and the maritime transport sector to enable sustainable development of the South Pacific region should be recognised as part of the energy and gender agenda as well as the unexplored field of research

Exploring How Sickle Cell Disease Impacts the Selection of Romantic Partner and Reproductive Decision Making of Adults with Sickle Cell Disease Living in The United Kingdom

This thesis is an empirical exploration of how Sickle Cell Disease (SCD) impacts the partner selection and reproductive decision making of adults with SCD living in the United Kingdom. Its impact on status disclosure and moral responsibility of the study population will also be elucidated. Drawing on qualitative interviews of 23 adults with SCD in the UK, I used the concepts of Embodied Risk, Social Model of Disability and Social Model of Relational Disability to explore and describe how embodying SCD impacts the lives of these individuals as they select partners for long term relationships and exercise agencies to make reproductive decisions. For study strategy, the participants were recruited from the target population as the experts since they are the ‘experiencers’ of the phenomenon being studied, to ensure that the research makes their voices heard rather than the voices of ‘Outsiders’ who are not embodied with SCD nor its burdens. I situate this analysis within a wider context of normal/abnormal, health/illness dichotomy created by the medical hegemonic culture that seeks to eliminate SCD from society while probably unintentionally neglecting the social, political and psychological oppressions of the target population. I argue that the impact of SCD on partner selection, reproductive decision making, status disclosure and moral responsibility of these adults living in the UK offers an understanding of the level of stereotyping, marginalization, discrimination and stigmatization this target group are subjected to as inaccurate genetic information is flung into society ‘unhinged’. The life course of these people whose bodies happen not to fit into culturally accepted norm for romantic partnership and reproduction are thereby ‘disrupted’. Findings reveal the widespread psycho-emotional disablism experienced by the participants and the ‘complex invisible works’ they perform as they struggle to find partners with whom to form romantic relationships and possibly parent children. These ‘works’ or ‘labours’ in their romantic spaces are embedded in the oppressive and partial information of the popular culture. This thesis brings to light these difficulties faced by people living with SCD, the restriction and isolation they experienced as they try to make family, bringing chaos and disruption to their life-pathways. The genetic screening result of the SCD-affected individual becomes defined and understood, not just as a biological phenomenon assumed by the NHS but by damaging consequences within the social domains of life. It is hoped that the thesis will contribute to the deconstruction of the inaccurate narratives of genetic information perpetuated by the dis/uninformed powers in the public forums that label SCD-affected persons as unsuitable for romantic partnerships and reproduction

Extending structures I: the level of groups

Let $H$ be a group and $E$ a set such that $H \subseteq E$. We shall describe and classify up to an isomorphism of groups that stabilizes $H$ the set of all group structures that can be defined on $E$ such that $H$ is a subgroup of $E$. A general product, which we call the unified product, is constructed such that both the crossed product and the bicrossed product of two groups are special cases of it. It is associated to $H$ and to a system $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$ called a group extending structure and we denote it by $H \ltimes S$. There exists a group structure on $E$ containing $H$ as a subgroup if and only if there exists an isomorphism of groups $(E, \cdot) \cong H \ltimes S$, for some group extending structure $\bigl((S, 1_S,\ast), \triangleleft, \, \triangleright, \, f \bigl)$. All such group structures on $E$ are classified up to an isomorphism of groups that stabilizes $H$ by a cohomological type set ${\mathcal K}^{2}_{\ltimes} (H, (S, 1_S))$. A Schreier type theorem is proved and an explicit example is given: it classifies up to an isomorphism that stabilizes $H$ all groups that contain $H$ as a subgroup of index 2.Comment: 17 pages; to appear in Algebras and Representation Theor

The time resolution of the St. Petersburg paradox

A resolution of the St. Petersburg paradox is presented. In contrast to the standard resolution, utility is not required. Instead, the time-average performance of the lottery is computed. The final result can be phrased mathematically identically to Daniel Bernoulli's resolution, which uses logarithmic utility, but is derived using a conceptually different argument. The advantage of the time resolution is the elimination of arbitrary utility functions.Comment: 20 pages, 1 figur

An Election Energy Threshold Based Multi-Hop Routing Protocol in a Grid-Clustered Wireless Sensor Network

Owing to the limited energy of sensor nodes (SNs) in a wireless sensor network (WSN), it is important to reduce and balance the energy consumption of the SNs in order to extend the WSN lifetime. Clustering mechanism is a highly efficient and effective mechanism for minimizing the amount of energy that SNs consume during the transmission of data packets. In this paper, an election energy threshold based multi-hop routing protocol (mEEMRP) is presented. In order to minimize energy consumption, this routing protocol uses grid clustering, where the network field is divided into grid clusters. SNs in each grid cluster select a cluster head (CH) based on a weight factor that takes the node location, node’s residual energy (RE) as well as the node’s distance from the base station into consideration. An energy efficient multi-hop routing algorithm is adopted during the transmission of data packets from the cluster heads (CHs) to the base station (BS). This multi-hop routing algorithm uses an election energy threshold value, T­nhCH that takes into consideration the RE of CHs as well as the distance between CHs. Simulation results show a 1.77% and 10.65% improvement in terms of network lifetime for two network field scenarios over Energy Efficient Multi-hop Routing Protocol (EEMRP)

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor