We give a detailed description of the arithmetic Fuchsian group of the Bolza surface and the associated quaternion order. This description enables us to show that the corresponding principal congruence covers satisfy the bound sys(X) > 4 3 log g(X) on the systole, where g is the genus. We also exhibit the Bolza group as a congruence subgroup, and calculate out a few examples of “Bolza twins” (u...

Let O1 be a (cocompact) Fuchsian group, given as the group of units of norm one in a maximal order O in an indefinite quaternion division algebra over Q. Using the (classical) Selberg trace formula, we show that the eigenvalues of the automorphic Laplacian for O1 and their multiplicities coincide with the eigenvalues and multiplicities of the Laplacian defined on the Maaß newforms for the Hecke...

The *congruence class of a least square solution for the following matrix equations AX = B, AXA = D, AXB = D and (AX XB) = (E F) is presented. Also, we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). Crown Copyrigh...

Recent healthcare literature has shown an increasing interest in spiritual care and the way in which it supports patients as they deal with illness; but; as the body of evidence grows in many areas; the spiritual aspects of day surgery have been under-researched. The aims of this interpretive phenomenological study were to identify the patients’ spiritual needs and concerns prior to surgery bot...

Purpose – Does celebrity endorsement work and how does it work among adolescents? This article aims to identity attributes of celebrity endorsers and attributes of celebrity endorsement advertisements that are most appealing to the adolescents. The article also examines adolescents’ perceptions about how celebrity-endorsement advertisements work. Method – A focus group study among 76 Chinese ad...

.Mmtract. In thL~ paper the first infinite series of translation nets with nonabelian translation groups and a large number of parallel classes are constructed. For that purpose we investigate partial congruence partitions (PCPs) with at least one normal component. Two series correspond to partial congruence partitions containing one normal elementary abelian component. The construction results...

It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincaré upper half-plane model H. To do this, one translates the congruence (or non-congruenc...

fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. in this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. we focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. at last, fuzzy completecongruen...

Objective: Theory and research suggest that the pursuit of personal goals that do not fit a person's affect-based implicit motives results in impaired emotional well-being, including increased symptoms of depression. The aim of this study was to evaluate an intervention designed to enhance motive-goal congruence and study its impact on well-being. Method: Seventy-four German students (mean age ...

An important and long-standing open problem in universal algebra asks whether every finite lattice is isomorphic to the congruence lattice of a finite algebra. Until this problem is resolved, our understanding of finite algebras is incomplete, since, given an arbitrary finite algebra, we cannot say whether there are any restrictions on the shape of its congruence lattice. If we find a finite la...