1,069 research outputs found
Hurwitz rational functions
A generalization of Hurwitz stable polynomials to real rational functions is
considered. We establishe an analogue of the Hurwitz stability criterion for
rational functions and introduce a new type of determinants that can be treated
as a generalization of the Hurwitz determinants.Comment: 10 page
Some New Addition Formulae for Weierstrass Elliptic Functions
We present new addition formulae for the Weierstrass functions associated
with a general elliptic curve. We prove the structure of the formulae in
n-variables and give the explicit addition formulae for the 2- and 3-variable
cases. These new results were inspired by new addition formulae found in the
case of an equianharmonic curve, which we can now observe as a specialisation
of the results here. The new formulae, and the techniques used to find them,
also follow the recent work for the generalisation of Weierstrass' functions to
curves of higher genus.Comment: 20 page
Quaternions and Special Relativity
We reformulate Special Relativity by a quaternionic algebra on reals. Using
{\em real linear quaternions}, we show that previous difficulties, concerning
the appropriate transformations on the space-time, may be overcome. This
implies that a complexified quaternionic version of Special Relativity is a
choice and not a necessity.Comment: 17 pages, latex, no figure
Martin Frobenius Ledermüllers, Hochfürstlich- Brandenburg- Culmbachischen Justiz-Raths ... Mikroskopische Gemüths- und Augen-Ergötzung : bestehend in Ein Hundert nach der Natur gezeichneten und mit Farben erleuchteten Kupfertafeln, Sammt deren Erklärung
Perencanaan dan Evaluasi User Interface untuk Aplikasi Tunanetra Berbasis Mobile Menggunakan Metode User Center Design dan QUIM Evaluation
Blind people are identified as someone who has limited vision. Difficulty in navigation is one of the problems faced by blind people when doing daily activities, one of which is the use of smartphones. In the development of the current technological era, the use of smartphones is very important where smartphones have the benefit of being able to be used and carried easily anytime and anywhere. However, not all applications are easy to use both in appearance and experience for blind people, because of the limitations that blind people have, this is because they have not paid attention to the user interface and user experience of blind users. One of them is the Gablind mobile application, which is an Internet of Thing (IoT) based application that is integrated with special glasses for visually impaired persons, which are used by blind people to navigate when doing activities outside. At the development stage of the Gablind application, planning requires both the user interface and the user experience, so that the features in the application can be used properly by blind people. This research focuses on the user, namely applying the user-centred design (UCD) method and the method of identifying usability using the QUIM factor. Based on the evaluation analysis of this study, the overall average value of the QUIM factor is 81.3%, so it is categorized as good. The factors that score <= 80% and above are usefulness, universality, accessibility, trustfulness, and learnability. Meanwhile, there are also factors that need to be improved because the value is less than 70%, namely productivity and satisfaction
Moduli space actions on the Hochschild Co-Chains of a Frobenius algebra I: Cell Operads
This is the first of two papers in which we prove that a cell model of the
moduli space of curves with marked points and tangent vectors at the marked
points acts on the Hochschild co--chains of a Frobenius algebra. We also prove
that a there is dg--PROP action of a version of Sullivan Chord diagrams which
acts on the normalized Hochschild co-chains of a Frobenius algebra. These
actions lift to operadic correlation functions on the co--cycles. In
particular, the PROP action gives an action on the homology of a loop space of
a compact simply--connected manifold.
In this first part, we set up the topological operads/PROPs and their cell
models. The main theorems of this part are that there is a cell model operad
for the moduli space of genus curves with punctures and a tangent
vector at each of these punctures and that there exists a CW complex whose
chains are isomorphic to a certain type of Sullivan Chord diagrams and that
they form a PROP. Furthermore there exist weak versions of these structures on
the topological level which all lie inside an all encompassing cyclic
(rational) operad.Comment: 50 pages, 7 figures. Newer version has minor changes. Some material
shifted. Typos and small things correcte
Octonionic Representations of GL(8,R) and GL(4,C)
Octonionic algebra being nonassociative is difficult to manipulate. We
introduce left-right octonionic barred operators which enable us to reproduce
the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an
interesting connection between the structure of left-right octonionic barred
operators and generic 4x4 complex matrices. As an application we give an
octonionic representation of the 4-dimensional Clifford algebra.Comment: 14 pages, Revtex, J. Math. Phys. (submitted
Spin Hurwitz numbers and topological quantum field theory
Spin Hurwitz numbers count ramified covers of a spin surface, weighted by the
size of their automorphism group (like ordinary Hurwitz numbers), but signed
according to the parity of the covering surface. These numbers were
first defined by Eskin-Okounkov-Pandharipande in order to study the moduli of
holomorphic differentials on a Riemann surface. They have also been related to
Gromov-Witten invariants of of complex 2-folds by work of Lee-Parker and
Maulik-Pandharipande. In this paper, we construct a (spin) TQFT which computes
these numbers, and deduce a formula for any genus in terms of the combinatorics
of the Sergeev algebra, generalizing the formula of
Eskin-Okounkov-Pandharipande. During the construction, we describe a procedure
for averaging any TQFT over finite covering spaces based on the finite path
integrals of Freed-Hopkins-Lurie-Teleman.Comment: 38 pages, substantially rewritten and reorganized following referees'
advice. Diagrams added. The key results are unchange
Development of high speed power thyristor: The gate assisted turn-off thyristor
A high speed power switch with unique turn-off capability was developed. This gate-assisted turn-off thyristor was rated at 609 V and 50 A with turn-off times of 2 microsec. Twenty-two units were delivered for evaluation in a series inverter circuit. In addition, test circuits designed to relate to the series inverter application were built and demonstrated
The singular linear preservers of non-singular matrices
Given an arbitrary field K, we reduce the determination of the singular
endomorphisms of M_n(K) that stabilize GL_n(K) to the classification of
n-dimensional division algebras over K. Our method, which is based upon
Dieudonn\'e's theorem on singular subspaces of M_n(K), also yields a proof for
the classical non-singular case.Comment: 12 pages, some minor corrections from the first versio
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